diff --git a/doc/modules/classification_threshold.rst b/doc/modules/classification_threshold.rst
index 712a094a43246..236c0736f7d23 100644
--- a/doc/modules/classification_threshold.rst
+++ b/doc/modules/classification_threshold.rst
@@ -143,7 +143,8 @@ Manually setting the decision threshold
 
 The previous sections discussed strategies to find an optimal decision threshold. It is
 also possible to manually set the decision threshold using the class
-:class:`~sklearn.model_selection.FixedThresholdClassifier`.
+:class:`~sklearn.model_selection.FixedThresholdClassifier`. In case that you don't want
+to refit the model when calling `fit`, you can set the parameter `prefit=True`.
 
 Examples
 --------
diff --git a/doc/whats_new/v1.6.rst b/doc/whats_new/v1.6.rst
index 87814e102ad98..dabe83fb53106 100644
--- a/doc/whats_new/v1.6.rst
+++ b/doc/whats_new/v1.6.rst
@@ -88,6 +88,14 @@ Changelog
   whether to raise an exception if a subset of the scorers in multimetric scoring fails
   or to return an error code. :pr:`28992` by :user:`Stefanie Senger <StefanieSenger>`.
 
+:mod:`sklearn.model_selection`
+..............................
+
+- |Enhancement| Add the parameter `prefit` to
+  :class:`model_selection.FixedThresholdClassifier` allowing the use of a pre-fitted
+  estimator without re-fitting it.
+  :pr:`29067` by :user:`Guillaume Lemaitre <glemaitre>`.
+
 Thanks to everyone who has contributed to the maintenance and improvement of
 the project since version 1.5, including:
 
diff --git a/sklearn/model_selection/_classification_threshold.py b/sklearn/model_selection/_classification_threshold.py
index e090a3d042746..1d221d3388434 100644
--- a/sklearn/model_selection/_classification_threshold.py
+++ b/sklearn/model_selection/_classification_threshold.py
@@ -271,6 +271,13 @@ class FixedThresholdClassifier(BaseThresholdClassifier):
           If the method is not implemented by the classifier, it will raise an
           error.
 
+    prefit : bool, default=False
+        Whether a pre-fitted model is expected to be passed into the constructor
+        directly or not. If `True`, `estimator` must be a fitted estimator. If `False`,
+        `estimator` is fitted and updated by calling `fit`.
+
+        .. versionadded:: 1.6
+
     Attributes
     ----------
     estimator_ : estimator instance
@@ -322,6 +329,7 @@ class FixedThresholdClassifier(BaseThresholdClassifier):
         **BaseThresholdClassifier._parameter_constraints,
         "threshold": [StrOptions({"auto"}), Real],
         "pos_label": [Real, str, "boolean", None],
+        "prefit": ["boolean"],
     }
 
     def __init__(
@@ -331,10 +339,12 @@ def __init__(
         threshold="auto",
         pos_label=None,
         response_method="auto",
+        prefit=False,
     ):
         super().__init__(estimator=estimator, response_method=response_method)
         self.pos_label = pos_label
         self.threshold = threshold
+        self.prefit = prefit
 
     def _fit(self, X, y, **params):
         """Fit the classifier.
@@ -357,7 +367,13 @@ def _fit(self, X, y, **params):
             Returns an instance of self.
         """
         routed_params = process_routing(self, "fit", **params)
-        self.estimator_ = clone(self.estimator).fit(X, y, **routed_params.estimator.fit)
+        if self.prefit:
+            check_is_fitted(self.estimator)
+            self.estimator_ = self.estimator
+        else:
+            self.estimator_ = clone(self.estimator).fit(
+                X, y, **routed_params.estimator.fit
+            )
         return self
 
     def predict(self, X):
diff --git a/sklearn/model_selection/tests/test_classification_threshold.py b/sklearn/model_selection/tests/test_classification_threshold.py
index f64edb2563c76..77c4c20e99ef2 100644
--- a/sklearn/model_selection/tests/test_classification_threshold.py
+++ b/sklearn/model_selection/tests/test_classification_threshold.py
@@ -1,7 +1,7 @@
 import numpy as np
 import pytest
 
-from sklearn.base import clone
+from sklearn.base import BaseEstimator, ClassifierMixin, clone
 from sklearn.datasets import (
     load_breast_cancer,
     load_iris,
@@ -682,3 +682,43 @@ def test_fixed_threshold_classifier_metadata_routing():
     classifier_default_threshold = FixedThresholdClassifier(estimator=clone(classifier))
     classifier_default_threshold.fit(X, y, sample_weight=sample_weight)
     assert_allclose(classifier_default_threshold.estimator_.coef_, classifier.coef_)
+
+
+class ClassifierLoggingFit(ClassifierMixin, BaseEstimator):
+    """Classifier that logs the number of `fit` calls."""
+
+    def __init__(self, fit_calls=0):
+        self.fit_calls = fit_calls
+
+    def fit(self, X, y, **fit_params):
+        self.fit_calls += 1
+        self.is_fitted_ = True
+        return self
+
+    def predict_proba(self, X):
+        return np.ones((X.shape[0], 2), np.float64)  # pragma: nocover
+
+
+def test_fixed_threshold_classifier_prefit():
+    """Check the behaviour of the `FixedThresholdClassifier` with the `prefit`
+    parameter."""
+    X, y = make_classification(random_state=0)
+
+    estimator = ClassifierLoggingFit()
+    model = FixedThresholdClassifier(estimator=estimator, prefit=True)
+    with pytest.raises(NotFittedError):
+        model.fit(X, y)
+
+    # check that we don't clone the classifier when `prefit=True`.
+    estimator.fit(X, y)
+    model.fit(X, y)
+    assert estimator.fit_calls == 1
+    assert model.estimator_ is estimator
+
+    # check that we clone the classifier when `prefit=False`.
+    estimator = ClassifierLoggingFit()
+    model = FixedThresholdClassifier(estimator=estimator, prefit=False)
+    model.fit(X, y)
+    assert estimator.fit_calls == 0
+    assert model.estimator_.fit_calls == 1
+    assert model.estimator_ is not estimator