diff --git a/doc/whats_new/v1.1.rst b/doc/whats_new/v1.1.rst
index 9c1084e393e8d..3aabed6214771 100644
--- a/doc/whats_new/v1.1.rst
+++ b/doc/whats_new/v1.1.rst
@@ -38,6 +38,13 @@ Changelog
     :pr:`123456` by :user:`Joe Bloggs <joeongithub>`.
     where 123456 is the *pull request* number, not the issue number.
 
+:mod:`sklearn.linear_model`
+...........................
+
+- |Fix| :class:`linear_model.LogisticRegression` now raises a better error
+  message when the solver does not support sparse matrices with int64 indices.
+  :pr:`21093` by `Tom Dupre la Tour`_.
+
 :mod:`sklearn.utils`
 ....................
 
diff --git a/sklearn/linear_model/_logistic.py b/sklearn/linear_model/_logistic.py
index 012d14102cae3..08e71edbc69ab 100644
--- a/sklearn/linear_model/_logistic.py
+++ b/sklearn/linear_model/_logistic.py
@@ -663,7 +663,7 @@ def _logistic_regression_path(
             X,
             accept_sparse="csr",
             dtype=np.float64,
-            accept_large_sparse=solver != "liblinear",
+            accept_large_sparse=solver not in ["liblinear", "sag", "saga"],
         )
         y = check_array(y, ensure_2d=False, dtype=None)
         check_consistent_length(X, y)
@@ -1511,7 +1511,7 @@ def fit(self, X, y, sample_weight=None):
             accept_sparse="csr",
             dtype=_dtype,
             order="C",
-            accept_large_sparse=solver != "liblinear",
+            accept_large_sparse=solver not in ["liblinear", "sag", "saga"],
         )
         check_classification_targets(y)
         self.classes_ = np.unique(y)
@@ -2080,7 +2080,7 @@ def fit(self, X, y, sample_weight=None):
             accept_sparse="csr",
             dtype=np.float64,
             order="C",
-            accept_large_sparse=solver != "liblinear",
+            accept_large_sparse=solver not in ["liblinear", "sag", "saga"],
         )
         check_classification_targets(y)
 
diff --git a/sklearn/linear_model/tests/test_logistic.py b/sklearn/linear_model/tests/test_logistic.py
index f900994081b47..1171613eb3718 100644
--- a/sklearn/linear_model/tests/test_logistic.py
+++ b/sklearn/linear_model/tests/test_logistic.py
@@ -2237,3 +2237,22 @@ def test_sample_weight_not_modified(multi_class, class_weight):
     )
     clf.fit(X, y, sample_weight=W)
     assert_allclose(expected, W)
+
+
+@pytest.mark.parametrize("solver", ["liblinear", "lbfgs", "newton-cg", "sag", "saga"])
+def test_large_sparse_matrix(solver):
+    # Solvers either accept large sparse matrices, or raise helpful error.
+    # Non-regression test for pull-request #21093.
+
+    # generate sparse matrix with int64 indices
+    X = sp.rand(20, 10, format="csr")
+    for attr in ["indices", "indptr"]:
+        setattr(X, attr, getattr(X, attr).astype("int64"))
+    y = np.random.randint(2, size=X.shape[0])
+
+    if solver in ["liblinear", "sag", "saga"]:
+        msg = "Only sparse matrices with 32-bit integer indices"
+        with pytest.raises(ValueError, match=msg):
+            LogisticRegression(solver=solver).fit(X, y)
+    else:
+        LogisticRegression(solver=solver).fit(X, y)