diff --git a/doc/whats_new/v1.1.rst b/doc/whats_new/v1.1.rst
index 98108f175b8fe..20801abbcdcbc 100644
--- a/doc/whats_new/v1.1.rst
+++ b/doc/whats_new/v1.1.rst
@@ -15,6 +15,10 @@ Changelog
 - |Fix| A default HTML representation is shown for meta-estimators with invalid
   parameters. :pr:`24015` by `Thomas Fan`_.
 
+- |Fix| Add support for F-contiguous arrays for estimators and functions whose back-end
+  have been changed in 1.1.
+  :pr:`23990` by :user:`Julien Jerphanion <jjerphan>`.
+
 :mod:`sklearn.base`
 ......................
 
diff --git a/sklearn/metrics/_pairwise_distances_reduction/_dispatcher.py b/sklearn/metrics/_pairwise_distances_reduction/_dispatcher.py
index a79fde694a9ed..1cf670ed35dec 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_dispatcher.py
+++ b/sklearn/metrics/_pairwise_distances_reduction/_dispatcher.py
@@ -80,11 +80,18 @@ def is_usable_for(cls, X, Y, metric) -> bool:
         True if the PairwiseDistancesReduction can be used, else False.
         """
         dtypes_validity = X.dtype == Y.dtype == np.float64
+        c_contiguity = (
+            hasattr(X, "flags")
+            and X.flags.c_contiguous
+            and hasattr(Y, "flags")
+            and Y.flags.c_contiguous
+        )
         return (
             get_config().get("enable_cython_pairwise_dist", True)
             and not issparse(X)
             and not issparse(Y)
             and dtypes_validity
+            and c_contiguity
             and metric in cls.valid_metrics()
         )
 
diff --git a/sklearn/metrics/tests/test_pairwise.py b/sklearn/metrics/tests/test_pairwise.py
index f14c558d5a3c1..31964e2d182dd 100644
--- a/sklearn/metrics/tests/test_pairwise.py
+++ b/sklearn/metrics/tests/test_pairwise.py
@@ -534,6 +534,14 @@ def test_pairwise_distances_argmin_min(dtype):
 
     assert_array_equal(argmin_0, argmin_1)
 
+    # F-contiguous arrays must be supported and must return identical results.
+    argmin_C_contiguous = pairwise_distances_argmin(X, Y)
+    argmin_F_contiguous = pairwise_distances_argmin(
+        np.asfortranarray(X), np.asfortranarray(Y)
+    )
+
+    assert_array_equal(argmin_C_contiguous, argmin_F_contiguous)
+
 
 def _reduce_func(dist, start):
     return dist[:, :100]
diff --git a/sklearn/metrics/tests/test_pairwise_distances_reduction.py b/sklearn/metrics/tests/test_pairwise_distances_reduction.py
index 57438b211918f..b8b7d584aee56 100644
--- a/sklearn/metrics/tests/test_pairwise_distances_reduction.py
+++ b/sklearn/metrics/tests/test_pairwise_distances_reduction.py
@@ -527,6 +527,9 @@ def test_pairwise_distances_reduction_is_usable_for():
     assert not PairwiseDistancesReduction.is_usable_for(csr_matrix(X), Y, metric)
     assert not PairwiseDistancesReduction.is_usable_for(X, csr_matrix(Y), metric)
 
+    # F-ordered arrays are not supported
+    assert not PairwiseDistancesReduction.is_usable_for(np.asfortranarray(X), Y, metric)
+
 
 def test_argkmin_factory_method_wrong_usages():
     rng = np.random.RandomState(1)
diff --git a/sklearn/tests/test_common.py b/sklearn/tests/test_common.py
index 185e9e1f61c79..1030f46607d33 100644
--- a/sklearn/tests/test_common.py
+++ b/sklearn/tests/test_common.py
@@ -18,6 +18,24 @@
 import pytest
 import numpy as np
 
+from sklearn.cluster import (
+    AffinityPropagation,
+    Birch,
+    MeanShift,
+    OPTICS,
+    SpectralClustering,
+)
+from sklearn.datasets import make_blobs
+from sklearn.manifold import Isomap, TSNE, LocallyLinearEmbedding
+from sklearn.neighbors import (
+    LocalOutlierFactor,
+    KNeighborsClassifier,
+    KNeighborsRegressor,
+    RadiusNeighborsClassifier,
+    RadiusNeighborsRegressor,
+)
+from sklearn.semi_supervised import LabelPropagation, LabelSpreading
+
 from sklearn.utils import all_estimators
 from sklearn.utils._testing import ignore_warnings
 from sklearn.exceptions import ConvergenceWarning
@@ -518,3 +536,44 @@ def test_check_param_validation(estimator):
         )
     _set_checking_parameters(estimator)
     check_param_validation(name, estimator)
+
+
+# TODO: remove this filter in 1.2
+@pytest.mark.filterwarnings("ignore::FutureWarning:sklearn")
+@pytest.mark.parametrize(
+    "Estimator",
+    [
+        AffinityPropagation,
+        Birch,
+        MeanShift,
+        KNeighborsClassifier,
+        KNeighborsRegressor,
+        RadiusNeighborsClassifier,
+        RadiusNeighborsRegressor,
+        LabelPropagation,
+        LabelSpreading,
+        OPTICS,
+        SpectralClustering,
+        LocalOutlierFactor,
+        LocallyLinearEmbedding,
+        Isomap,
+        TSNE,
+    ],
+)
+def test_f_contiguous_array_estimator(Estimator):
+    # Non-regression test for:
+    # https://github.com/scikit-learn/scikit-learn/issues/23988
+    # https://github.com/scikit-learn/scikit-learn/issues/24013
+
+    X, _ = make_blobs(n_samples=80, n_features=4, random_state=0)
+    X = np.asfortranarray(X)
+    y = np.round(X[:, 0])
+
+    est = Estimator()
+    est.fit(X, y)
+
+    if hasattr(est, "transform"):
+        est.transform(X)
+
+    if hasattr(est, "predict"):
+        est.predict(X)