diff --git a/doc/whats_new/v1.1.rst b/doc/whats_new/v1.1.rst
index 5d49a6fd281c7..daec37e96ac16 100644
--- a/doc/whats_new/v1.1.rst
+++ b/doc/whats_new/v1.1.rst
@@ -110,6 +110,13 @@ Changelog
   reconstruction of a `X` target when a `Y` parameter is given. :pr:`19680` by
   :user:`Robin Thibaut <robinthibaut>`.
 
+:mod:`sklearn.discriminant_analysis`
+....................................
+
+- |API| Adds :term:`get_feature_names_out` to
+  :class:`discriminant_analysis.LinearDiscriminantAnalysis`. :pr:`22120` by
+  `Thomas Fan`_.
+
 :mod:`sklearn.feature_extraction`
 .................................
 
diff --git a/sklearn/discriminant_analysis.py b/sklearn/discriminant_analysis.py
index 79faa8694a535..65960bd044a30 100644
--- a/sklearn/discriminant_analysis.py
+++ b/sklearn/discriminant_analysis.py
@@ -15,6 +15,7 @@
 from scipy.special import expit
 
 from .base import BaseEstimator, TransformerMixin, ClassifierMixin
+from .base import _ClassNamePrefixFeaturesOutMixin
 from .linear_model._base import LinearClassifierMixin
 from .covariance import ledoit_wolf, empirical_covariance, shrunk_covariance
 from .utils.multiclass import unique_labels
@@ -165,7 +166,10 @@ def _class_cov(X, y, priors, shrinkage=None, covariance_estimator=None):
 
 
 class LinearDiscriminantAnalysis(
-    LinearClassifierMixin, TransformerMixin, BaseEstimator
+    _ClassNamePrefixFeaturesOutMixin,
+    LinearClassifierMixin,
+    TransformerMixin,
+    BaseEstimator,
 ):
     """Linear Discriminant Analysis.
 
@@ -614,6 +618,7 @@ def fit(self, X, y):
             self.intercept_ = np.array(
                 self.intercept_[1] - self.intercept_[0], ndmin=1, dtype=X.dtype
             )
+        self._n_features_out = self._max_components
         return self
 
     def transform(self, X):
diff --git a/sklearn/tests/test_common.py b/sklearn/tests/test_common.py
index 3611d52085b9e..2a0bb8d085b77 100644
--- a/sklearn/tests/test_common.py
+++ b/sklearn/tests/test_common.py
@@ -382,7 +382,6 @@ def test_pandas_column_name_consistency(estimator):
 GET_FEATURES_OUT_MODULES_TO_IGNORE = [
     "cluster",
     "cross_decomposition",
-    "discriminant_analysis",
     "ensemble",
     "isotonic",
     "kernel_approximation",
diff --git a/sklearn/tests/test_discriminant_analysis.py b/sklearn/tests/test_discriminant_analysis.py
index 90e5b57a63779..40ede1feba547 100644
--- a/sklearn/tests/test_discriminant_analysis.py
+++ b/sklearn/tests/test_discriminant_analysis.py
@@ -650,3 +650,20 @@ def test_raises_value_error_on_same_number_of_classes_and_samples(solver):
     clf = LinearDiscriminantAnalysis(solver=solver)
     with pytest.raises(ValueError, match="The number of samples must be more"):
         clf.fit(X, y)
+
+
+def test_get_feature_names_out():
+    """Check get_feature_names_out uses class name as prefix."""
+
+    est = LinearDiscriminantAnalysis().fit(X, y)
+    names_out = est.get_feature_names_out()
+
+    class_name_lower = "LinearDiscriminantAnalysis".lower()
+    expected_names_out = np.array(
+        [
+            f"{class_name_lower}{i}"
+            for i in range(est.explained_variance_ratio_.shape[0])
+        ],
+        dtype=object,
+    )
+    assert_array_equal(names_out, expected_names_out)