diff --git a/build_tools/azure/pylatest_conda_forge_mkl_linux-64_conda.lock b/build_tools/azure/pylatest_conda_forge_mkl_linux-64_conda.lock
index a9ea47c37078e..600f32ce525d1 100644
--- a/build_tools/azure/pylatest_conda_forge_mkl_linux-64_conda.lock
+++ b/build_tools/azure/pylatest_conda_forge_mkl_linux-64_conda.lock
@@ -1,20 +1,21 @@
 # Generated by conda-lock.
 # platform: linux-64
-# input_hash: 15de7a0d1a0d046ada825ffa5ad3547c790bf903bd5d9b03e7c0e9a6a62c680d
+# input_hash: 96e0d4e2ab4d0a2d543fdc457c546ea2815a9a4581e6e2190c35f0ef1a6812c0
 @EXPLICIT
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@@ -22,7 +23,7 @@ https://conda.anaconda.org/conda-forge/linux-64/libopengl-1.7.0-ha4b6fd6_2.conda
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@@ -38,7 +39,7 @@ https://conda.anaconda.org/conda-forge/linux-64/libuv-1.50.0-hb9d3cd8_0.conda#77
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+https://conda.anaconda.org/conda-forge/noarch/dask-2025.3.0-pyhd8ed1ab_0.conda#95e33679c10ef9ef65df0fc01a71fdc5
diff --git a/build_tools/azure/pylatest_conda_forge_mkl_linux-64_environment.yml b/build_tools/azure/pylatest_conda_forge_mkl_linux-64_environment.yml
index e804bf1ce8e31..69365c4cee03b 100644
--- a/build_tools/azure/pylatest_conda_forge_mkl_linux-64_environment.yml
+++ b/build_tools/azure/pylatest_conda_forge_mkl_linux-64_environment.yml
@@ -23,6 +23,7 @@ dependencies:
   - pytest-cov
   - coverage
   - ccache
+  - dask
   - pytorch
   - pytorch-cpu
   - polars
diff --git a/build_tools/update_environments_and_lock_files.py b/build_tools/update_environments_and_lock_files.py
index 0edf62b5a0d7b..5f716cb9f0aea 100644
--- a/build_tools/update_environments_and_lock_files.py
+++ b/build_tools/update_environments_and_lock_files.py
@@ -118,6 +118,7 @@ def remove_from(alist, to_remove):
         "conda_dependencies": common_dependencies
         + [
             "ccache",
+            "dask",
             "pytorch",
             "pytorch-cpu",
             "polars",
diff --git a/doc/modules/array_api.rst b/doc/modules/array_api.rst
index b4940eccec2fc..a545a17ca8120 100644
--- a/doc/modules/array_api.rst
+++ b/doc/modules/array_api.rst
@@ -36,6 +36,10 @@ explicitly as explained in the following.
     Currently, only `array-api-strict`, `cupy`, and `PyTorch` are known to work
     with scikit-learn's estimators.
 
+    `dask.array` support is incomplete at the time of writing: some methods and
+    estimators may not work while we work out a way to handle Dask's lazy evaluation
+    semantics in a library-agnostic way.
+
 The following video provides an overview of the standard's design principles
 and how it facilitates interoperability between array libraries:
 
diff --git a/doc/whats_new/v1.5.rst b/doc/whats_new/v1.5.rst
index 1ce5aa4839426..f6658b47fca44 100644
--- a/doc/whats_new/v1.5.rst
+++ b/doc/whats_new/v1.5.rst
@@ -211,6 +211,11 @@ See :ref:`array_api` for more details.
 
 **Classes:**
 
+**Libraries:**
+
+- ``dask.array`` is now experimentally supported as an array API backend.
+  Some methods and estimators may not work with dask.
+  :pr:`28588` by :user:`Thomas Li <lithomas1>`
 - :class:`linear_model.Ridge` now supports the Array API for the `svd` solver.
   See :ref:`array_api` for more details.
   :pr:`27800` by :user:`Franck Charras <fcharras>`, :user:`Olivier Grisel <ogrisel>`
diff --git a/sklearn/_min_dependencies.py b/sklearn/_min_dependencies.py
index 03fd53d047249..e0a4228a8bedc 100644
--- a/sklearn/_min_dependencies.py
+++ b/sklearn/_min_dependencies.py
@@ -19,6 +19,7 @@
 # It will NOT be included in setup's extras_require
 # The values are (version_spec, comma separated tags)
 dependent_packages = {
+    "array-api-compat": ("1.5.1", "tests"),
     "numpy": (NUMPY_MIN_VERSION, "build, install"),
     "scipy": (SCIPY_MIN_VERSION, "build, install"),
     "joblib": (JOBLIB_MIN_VERSION, "install"),
diff --git a/sklearn/conftest.py b/sklearn/conftest.py
index 6af3a2a51c0ce..2c6910dab5c1d 100644
--- a/sklearn/conftest.py
+++ b/sklearn/conftest.py
@@ -363,6 +363,27 @@ def print_changed_only_false():
     set_config(print_changed_only=True)  # reset to default
 
 
+@pytest.fixture
+def skip_dask_array_api_compliance(request):
+    """
+    Xfails an array API compliance test for dask.
+    (i.e. when the array_namespace fixture yields 'dask.array')
+
+    When using this fixture, please insert a comment to explain what particular
+    aspect of Dask is preventing the tests to pass, e.g. missing module level
+    function or array level method, value-dependent shape item values or array
+    assignments with a value-dependent boolean mask.
+    """
+    array_namespace = request.getfixturevalue("array_namespace")
+    if array_namespace == "dask.array":
+        pytest.skip(
+            reason=(
+                "Estimator/method does not work because of dask array API compliance"
+                " issues"
+            )
+        )
+
+
 if dt_config is not None:
     # Strict mode to differentiate between 3.14 and np.float64(3.14)
     dt_config.strict_check = True
diff --git a/sklearn/decomposition/_base.py b/sklearn/decomposition/_base.py
index 13202d56c50f4..70be5753bcb79 100644
--- a/sklearn/decomposition/_base.py
+++ b/sklearn/decomposition/_base.py
@@ -47,7 +47,7 @@ def get_covariance(self):
             xp.asarray(0.0, device=device(exp_var), dtype=exp_var.dtype),
         )
         cov = (components_.T * exp_var_diff) @ components_
-        _fill_or_add_to_diagonal(cov, self.noise_variance_, xp)
+        cov = _fill_or_add_to_diagonal(cov, self.noise_variance_, xp)
         return cov
 
     def get_precision(self):
@@ -89,10 +89,10 @@ def get_precision(self):
             xp.asarray(0.0, device=device(exp_var)),
         )
         precision = components_ @ components_.T / self.noise_variance_
-        _fill_or_add_to_diagonal(precision, 1.0 / exp_var_diff, xp)
+        precision = _fill_or_add_to_diagonal(precision, 1.0 / exp_var_diff, xp)
         precision = components_.T @ linalg_inv(precision) @ components_
         precision /= -(self.noise_variance_**2)
-        _fill_or_add_to_diagonal(precision, 1.0 / self.noise_variance_, xp)
+        precision = _fill_or_add_to_diagonal(precision, 1.0 / self.noise_variance_, xp)
         return precision
 
     @abstractmethod
diff --git a/sklearn/decomposition/tests/test_pca.py b/sklearn/decomposition/tests/test_pca.py
index 2b97138c4dea3..8b5608dd94bfb 100644
--- a/sklearn/decomposition/tests/test_pca.py
+++ b/sklearn/decomposition/tests/test_pca.py
@@ -13,6 +13,7 @@
 from sklearn.decomposition import PCA
 from sklearn.decomposition._pca import _assess_dimension, _infer_dimension
 from sklearn.utils._array_api import (
+    _array_api_skips,
     _atol_for_type,
     _convert_to_numpy,
     _get_namespace_device_dtype_ids,
@@ -1036,8 +1037,14 @@ def check_array_api_get_precision(name, estimator, array_namespace, device, dtyp
 def test_pca_array_api_compliance(
     estimator, check, array_namespace, device, dtype_name
 ):
+    skip_methods = _array_api_skips["PCA"]
     name = estimator.__class__.__name__
-    check(name, estimator, array_namespace, device=device, dtype_name=dtype_name)
+    kwargs = {}
+    if check is check_array_api_input_and_values:
+        kwargs = {"skip_methods": skip_methods}
+    check(
+        name, estimator, array_namespace, device=device, dtype_name=dtype_name, **kwargs
+    )
 
 
 @pytest.mark.parametrize(
diff --git a/sklearn/discriminant_analysis.py b/sklearn/discriminant_analysis.py
index 6df26a05a8781..d13960ad0c7c9 100644
--- a/sklearn/discriminant_analysis.py
+++ b/sklearn/discriminant_analysis.py
@@ -20,7 +20,7 @@
 from .covariance import empirical_covariance, ledoit_wolf, shrunk_covariance
 from .linear_model._base import LinearClassifierMixin
 from .preprocessing import StandardScaler
-from .utils._array_api import _expit, device, get_namespace, size
+from .utils._array_api import _expit, device, get_namespace, size, xpx
 from .utils._param_validation import HasMethods, Interval, StrOptions
 from .utils.extmath import softmax
 from .utils.multiclass import check_classification_targets, unique_labels
@@ -106,11 +106,12 @@ def _class_means(X, y):
         Class means.
     """
     xp, is_array_api_compliant = get_namespace(X)
-    classes, y = xp.unique_inverse(y)
-    means = xp.zeros((classes.shape[0], X.shape[1]), device=device(X), dtype=X.dtype)
+    n_classes = xpx.nunique(y)
+    _, y = xp.unique_inverse(y)
+    means = xp.zeros((n_classes, X.shape[1]), device=device(X), dtype=X.dtype)
 
     if is_array_api_compliant:
-        for i in range(classes.shape[0]):
+        for i in range(n_classes):
             means[i, :] = xp.mean(X[y == i], axis=0)
     else:
         # TODO: Explore the choice of using bincount + add.at as it seems sub optimal
@@ -577,20 +578,29 @@ def _solve_svd(self, X, y):
             svd = scipy.linalg.svd
 
         n_samples, n_features = X.shape
-        n_classes = self.classes_.shape[0]
+        # TODO: this is a duplicate computation
+        # in
+        n_classes = int(xpx.nunique(y))
 
         self.means_ = _class_means(X, y)
         if self.store_covariance:
             self.covariance_ = _class_cov(X, y, self.priors_)
 
-        Xc = []
-        for idx, group in enumerate(self.classes_):
-            Xg = X[y == group]
-            Xc.append(Xg - self.means_[idx, :])
-
-        self.xbar_ = self.priors_ @ self.means_
-
-        Xc = xp.concat(Xc, axis=0)
+        def calc_xc(classes):
+            Xc = []
+            for idx, group in enumerate(classes):
+                Xg = X[y == group]
+                Xc.append(Xg - self.means_[idx, :])
+            Xc = xp.concat(Xc, axis=0)
+            return Xc
+
+        Xc = xpx.lazy_apply(calc_xc, self.classes_, shape=(n_samples, n_features))
+        self.xbar_ = xpx.lazy_apply(
+            lambda priors, means: priors @ means,
+            self.priors_,
+            self.means_,
+            shape=(n_classes, n_features),
+        )
 
         # 1) within (univariate) scaling by with classes std-dev
         std = xp.std(Xc, axis=0)
diff --git a/sklearn/linear_model/_ridge.py b/sklearn/linear_model/_ridge.py
index c22690b2b01c6..52da97a5a9fc4 100644
--- a/sklearn/linear_model/_ridge.py
+++ b/sklearn/linear_model/_ridge.py
@@ -287,10 +287,13 @@ def _solve_svd(X, y, alpha, xp=None):
     xp, _ = get_namespace(X, xp=xp)
     U, s, Vt = xp.linalg.svd(X, full_matrices=False)
     idx = s > 1e-15  # same default value as scipy.linalg.pinv
-    s_nnz = s[idx][:, None]
+    s = s[:, None]
     UTy = U.T @ y
     d = xp.zeros((s.shape[0], alpha.shape[0]), dtype=X.dtype, device=device(X))
-    d[idx] = s_nnz / (s_nnz**2 + alpha)
+
+    # Use where to do the equivalent of boolean indexing for
+    d = xp.where(idx[:, None], s / (s**2 + alpha), d)
+
     d_UT_y = d * UTy
     return (Vt.T @ d_UT_y).T
 
diff --git a/sklearn/metrics/_regression.py b/sklearn/metrics/_regression.py
index 9be9f1d954fcc..8f2d8ac821bc5 100644
--- a/sklearn/metrics/_regression.py
+++ b/sklearn/metrics/_regression.py
@@ -951,8 +951,8 @@ def _assemble_r2_explained_variance(
         # Non-zero Numerator and Non-zero Denominator: use the formula
         valid_score = nonzero_denominator & nonzero_numerator
 
-        output_scores[valid_score] = 1 - (
-            numerator[valid_score] / denominator[valid_score]
+        output_scores = xp.where(
+            valid_score, 1 - numerator / denominator, output_scores
         )
 
         # Non-zero Numerator and Zero Denominator:
diff --git a/sklearn/metrics/pairwise.py b/sklearn/metrics/pairwise.py
index cca8f2b6ae1c7..209155594c1df 100644
--- a/sklearn/metrics/pairwise.py
+++ b/sklearn/metrics/pairwise.py
@@ -433,7 +433,7 @@ def _euclidean_distances(X, Y, X_norm_squared=None, Y_norm_squared=None, squared
     # Ensure that distances between vectors and themselves are set to 0.0.
     # This may not be the case due to floating point rounding errors.
     if X is Y:
-        _fill_or_add_to_diagonal(distances, 0, xp=xp, add_value=False)
+        distances = _fill_or_add_to_diagonal(distances, 0, xp=xp, add_value=False)
 
     if squared:
         return distances
@@ -1171,7 +1171,7 @@ def cosine_distances(X, Y=None):
     if X is Y or Y is None:
         # Ensure that distances between vectors and themselves are set to 0.0.
         # This may not be the case due to floating point rounding errors.
-        _fill_or_add_to_diagonal(S, 0.0, xp, add_value=False)
+        S = _fill_or_add_to_diagonal(S, 0.0, xp, add_value=False)
     return S
 
 
diff --git a/sklearn/metrics/tests/test_common.py b/sklearn/metrics/tests/test_common.py
index 6f9e11d4f4780..ab8a8094bfb93 100644
--- a/sklearn/metrics/tests/test_common.py
+++ b/sklearn/metrics/tests/test_common.py
@@ -72,6 +72,7 @@
 from sklearn.preprocessing import LabelBinarizer
 from sklearn.utils import shuffle
 from sklearn.utils._array_api import (
+    _array_api_skips,
     _atol_for_type,
     _convert_to_numpy,
     _get_namespace_device_dtype_ids,
@@ -1843,6 +1844,12 @@ def test_metrics_pos_label_error_str(metric, y_pred_threshold, dtype_y_str):
 def check_array_api_metric(
     metric, array_namespace, device, dtype_name, a_np, b_np, **metric_kwargs
 ):
+    func_name = metric.func.__name__ if isinstance(metric, partial) else metric.__name__
+    if _array_api_skips.get(func_name, {}).get(array_namespace) == "all":
+        pytest.skip(
+            f"{array_namespace} is not Array API compliant for {metric.__name__}"
+        )
+
     xp = _array_api_for_tests(array_namespace, device)
 
     a_xp = xp.asarray(a_np, device=device)
diff --git a/sklearn/utils/_array_api.py b/sklearn/utils/_array_api.py
index 48c941f3c6e85..7f25730490d22 100644
--- a/sklearn/utils/_array_api.py
+++ b/sklearn/utils/_array_api.py
@@ -16,12 +16,27 @@
 from .._config import get_config
 from ..externals import array_api_compat
 from ..externals import array_api_extra as xpx
+from ..externals.array_api_compat import is_dask_namespace, is_lazy_array
 from ..externals.array_api_compat import numpy as np_compat
 from .fixes import parse_version
 
 # TODO: complete __all__
 __all__ = ["xpx"]  # we import xpx here just to re-export it, need this to appease ruff
 
+# Dictionary listing the methods/estimators to skip
+# testing for a certain array api namespace
+
+# use "all" to skip all testing for an estimator/method
+# for a namespace (not just specific methods)
+# (see the dask.array skip in LinearDiscriminantAnalysis for an example of this)
+_array_api_skips = {
+    # Dask doesn't implement slogdet from the Array API
+    # which is used in score/score_samples
+    "PCA": {"dask.array": ["score", "score_samples"]},
+    # Lazy evaluation semantics: value-dependent shape item value (nan):
+    # "LinearDiscriminantAnalysis": {"dask.array": "all"},
+}
+
 _NUMPY_NAMESPACE_NAMES = {"numpy", "sklearn.externals.array_api_compat.numpy"}
 
 
@@ -50,6 +65,7 @@ def yield_namespaces(include_numpy_namespaces=True):
         "array_api_strict",
         "cupy",
         "torch",
+        "dask.array",
     ]:
         if not include_numpy_namespaces and array_namespace in _NUMPY_NAMESPACE_NAMES:
             continue
@@ -543,6 +559,10 @@ def _fill_or_add_to_diagonal(array, value, xp, add_value=True, wrap=False):
         )
 
     value = xp.asarray(value, dtype=array.dtype, device=device(array))
+
+    # TODO: candidate for upstreaming to array-api-extra
+    # This can't work in-place for dask/jax
+
     end = None
     # Explicit, fast formula for the common case.  For 2-d arrays, we
     # accept rectangular ones.
@@ -555,6 +575,10 @@ def _fill_or_add_to_diagonal(array, value, xp, add_value=True, wrap=False):
         array_flat[:end:step] += value
     else:
         array_flat[:end:step] = value
+    if is_dask_namespace(xp):
+        # hack to make sure correct value is returned for dask
+        return xp.reshape(array_flat, array.shape)
+    return array
 
 
 def _is_xp_namespace(xp, name):
@@ -621,13 +645,15 @@ def _average(a, axis=None, weights=None, normalize=True, xp=None):
         weights = xp.asarray(weights, device=device_)
 
     if weights is not None and a.shape != weights.shape:
-        if axis is None:
+        # shape checks are disabled here for dask
+        # TODO: figure out a strategy for doing this across sklearn
+        if axis is None and not is_lazy_array(a):
             raise TypeError(
                 f"Axis must be specified when the shape of a {tuple(a.shape)} and "
                 f"weights {tuple(weights.shape)} differ."
             )
 
-        if tuple(weights.shape) != (a.shape[axis],):
+        if tuple(weights.shape) != (a.shape[axis],) and not is_lazy_array(a):
             raise ValueError(
                 f"Shape of weights weights.shape={tuple(weights.shape)} must be "
                 f"consistent with a.shape={tuple(a.shape)} and {axis=}."
@@ -910,6 +936,10 @@ def _in1d(ar1, ar2, xp, assume_unique=False, invert=False):
     present in numpy:
     https://github.com/numpy/numpy/blob/v1.26.0/numpy/lib/arraysetops.py#L524-L758
     """
+    if is_dask_namespace(xp):
+        import dask.array as da
+
+        return da.isin(ar1, ar2, assume_unique, invert)
     xp, _ = get_namespace(ar1, ar2, xp=xp)
 
     # This code is run to make the code significantly faster
diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index 5142de2348e2a..b29e968cff0f0 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -64,6 +64,7 @@
 from ..preprocessing import StandardScaler, scale
 from ..utils import _safe_indexing
 from ..utils._array_api import (
+    _array_api_skips,
     _atol_for_type,
     _convert_to_numpy,
     get_namespace,
@@ -349,6 +350,7 @@ def _yield_array_api_checks(estimator):
             array_namespace=array_namespace,
             dtype_name=dtype_name,
             device=device,
+            skips=_array_api_skips.get(estimator.__class__.__name__, {}),
         )
 
 
@@ -1040,6 +1042,7 @@ def check_array_api_input(
     name,
     estimator_orig,
     array_namespace,
+    skips,
     device=None,
     dtype_name="float64",
     check_values=False,
@@ -1051,7 +1054,14 @@ def check_array_api_input(
 
     When check_values is True, it also checks that calling the estimator on the
     array_api Array gives the same results as ndarrays.
+
+    skips is a dictionary mapping the name of the array_namespace to skip to
+    the names of the methods to skip (for estimators), or the string "all"
+    (to skip all methods for this estimator)
     """
+    if skips.get(array_namespace) == "all":
+        raise SkipTest(f"{array_namespace} is not Array API compliant for {name}")
+
     xp = _array_api_for_tests(array_namespace, device)
 
     X, y = make_classification(random_state=42)
@@ -1112,6 +1122,7 @@ def check_array_api_input(
         "transform",
     )
 
+    methods_to_skip = skips.get(array_namespace, [])
     try:
         np.asarray(X_xp)
         np.asarray(y_xp)
@@ -1148,8 +1159,11 @@ def check_array_api_input(
 
     for method_name in methods:
         method = getattr(est, method_name, None)
-        if method is None:
-            continue
+        if method is None or method_name in methods_to_skip:
+            raise SkipTest(
+                f"{array_namespace} is not Array API compliant for method"
+                f" {method_name} of {name}"
+            )
 
         if method_name == "score":
             result = method(X, y)
@@ -1159,6 +1173,8 @@ def check_array_api_input(
             assert isinstance(result, float)
             assert isinstance(result_xp, float)
             if check_values:
+                print(result)
+                print(result_xp)
                 assert abs(result - result_xp) < _atol_for_type(X.dtype)
             continue
         else:
@@ -1219,6 +1235,7 @@ def check_array_api_input_and_values(
     array_namespace,
     device=None,
     dtype_name="float64",
+    skip_methods={},
 ):
     return check_array_api_input(
         name,
@@ -1227,6 +1244,7 @@ def check_array_api_input_and_values(
         device=device,
         dtype_name=dtype_name,
         check_values=True,
+        skips=skip_methods,
     )
 
 
diff --git a/sklearn/utils/multiclass.py b/sklearn/utils/multiclass.py
index 6c089069387be..5e4e5e485e44e 100644
--- a/sklearn/utils/multiclass.py
+++ b/sklearn/utils/multiclass.py
@@ -10,7 +10,7 @@
 import numpy as np
 from scipy.sparse import issparse
 
-from ..utils._array_api import get_namespace
+from ..utils._array_api import get_namespace, xpx
 from ..utils.fixes import VisibleDeprecationWarning
 from ._unique import attach_unique, cached_unique
 from .validation import _assert_all_finite, check_array
@@ -190,11 +190,12 @@ def is_multilabel(y):
             and (y.dtype.kind in "biu" or _is_integral_float(labels))  # bool, int, uint
         )
     else:
-        labels = cached_unique(y, xp=xp)
+        # TODO: caching?
+        # labels = cached_unique(y, xp=xp)
 
-        return labels.shape[0] < 3 and (
+        return int(xpx.nunique(y)) < 3 and (
             xp.isdtype(y.dtype, ("bool", "signed integer", "unsigned integer"))
-            or _is_integral_float(labels)
+            or _is_integral_float(y)
         )
 
 
@@ -418,7 +419,8 @@ def _raise_or_return():
     # Check multiclass
     if issparse(first_row_or_val):
         first_row_or_val = first_row_or_val.data
-    if cached_unique(y).shape[0] > 2 or (y.ndim == 2 and len(first_row_or_val) > 1):
+    # cast to int to force computation for Dask
+    if int(xpx.nunique(y)) > 2 or (y.ndim == 2 and len(first_row_or_val) > 1):
         # [1, 2, 3] or [[1., 2., 3]] or [[1, 2]]
         return "multiclass" + suffix
     else:
diff --git a/sklearn/utils/tests/test_array_api.py b/sklearn/utils/tests/test_array_api.py
index 164e3024a31e7..8bbfbcbd38346 100644
--- a/sklearn/utils/tests/test_array_api.py
+++ b/sklearn/utils/tests/test_array_api.py
@@ -583,7 +583,9 @@ def test_fill_or_add_to_diagonal(array_namespace, device_, dtype_name, wrap):
     xp = _array_api_for_tests(array_namespace, device_)
     array_np = numpy.zeros((5, 4), dtype=numpy.int64)
     array_xp = xp.asarray(array_np)
-    _fill_or_add_to_diagonal(array_xp, value=1, xp=xp, add_value=False, wrap=wrap)
+    array_xp = _fill_or_add_to_diagonal(
+        array_xp, value=1, xp=xp, add_value=False, wrap=wrap
+    )
     numpy.fill_diagonal(array_np, val=1, wrap=wrap)
     assert_array_equal(_convert_to_numpy(array_xp, xp=xp), array_np)
 
diff --git a/sklearn/utils/tests/test_estimator_checks.py b/sklearn/utils/tests/test_estimator_checks.py
index 4e573c8d1793f..bb63d90eb6135 100644
--- a/sklearn/utils/tests/test_estimator_checks.py
+++ b/sklearn/utils/tests/test_estimator_checks.py
@@ -584,6 +584,7 @@ def test_check_array_api_input():
             "BrokenArrayAPI",
             BrokenArrayAPI(),
             array_namespace="array_api_strict",
+            skips={},
             check_values=True,
         )
 
diff --git a/sklearn/utils/tests/test_multiclass.py b/sklearn/utils/tests/test_multiclass.py
index e361a93e41b10..d44994d9b961f 100644
--- a/sklearn/utils/tests/test_multiclass.py
+++ b/sklearn/utils/tests/test_multiclass.py
@@ -39,6 +39,8 @@
 multilabel_explicit_zero = np.array([[0, 1], [1, 0]])
 multilabel_explicit_zero[:, 0] = 0
 
+skip_dask = pytest.mark.usefixtures("skip_dask_array_api_compliance")
+
 
 def _generate_sparse(
     data,
@@ -382,6 +384,7 @@ def test_is_multilabel():
             ), f"is_multilabel({example!r}) should be {dense_exp}"
 
 
+@skip_dask  # lazy evaluation semantics for value-dependent shape values
 @pytest.mark.parametrize(
     "array_namespace, device, dtype_name",
     yield_namespace_device_dtype_combinations(),