diff --git a/sklearn/metrics/_dist_metrics.pyx.tp b/sklearn/metrics/_dist_metrics.pyx.tp
index c317605f94d14..b7d3d1f4d86a6 100644
--- a/sklearn/metrics/_dist_metrics.pyx.tp
+++ b/sklearn/metrics/_dist_metrics.pyx.tp
@@ -42,15 +42,24 @@ BOOL_METRICS = [
     "dice",
     "rogerstanimoto",
     "russellrao",
-    "sokalmichener",
     "sokalsneath",
 ]
+DEPRECATED_METRICS = []
+if sp_base_version < parse_version("1.17"):
+    # Deprecated in SciPy 1.15 and removed in SciPy 1.17
+    BOOL_METRICS += ["sokalmichener"]
+if sp_base_version >= parse_version("1.15"):
+    DEPRECATED_METRICS.append("sokalmichener")
 if sp_base_version < parse_version("1.11"):
     # Deprecated in SciPy 1.9 and removed in SciPy 1.11
     BOOL_METRICS += ["kulsinski"]
+if sp_base_version >= parse_version("1.9"):
+    DEPRECATED_METRICS.append("kulsinski")
 if sp_base_version < parse_version("1.9"):
     # Deprecated in SciPy 1.0 and removed in SciPy 1.9
     BOOL_METRICS += ["matching"]
+if sp_base_version >= parse_version("1.0"):
+    DEPRECATED_METRICS.append("matching")
 
 def get_valid_metric_ids(L):
     """Given an iterable of metric class names or class identifiers,
diff --git a/sklearn/metrics/pairwise.py b/sklearn/metrics/pairwise.py
index 8b4f35a8195c2..9b62a0f73f130 100644
--- a/sklearn/metrics/pairwise.py
+++ b/sklearn/metrics/pairwise.py
@@ -693,7 +693,6 @@ def _argmin_reduce(dist, start):
     "rogerstanimoto",
     "russellrao",
     "seuclidean",
-    "sokalmichener",
     "sokalsneath",
     "sqeuclidean",
     "yule",
@@ -701,6 +700,9 @@ def _argmin_reduce(dist, start):
     "nan_euclidean",
     "haversine",
 ]
+if sp_base_version < parse_version("1.17"):  # pragma: no cover
+    # Deprecated in SciPy 1.15 and removed in SciPy 1.17
+    _VALID_METRICS += ["sokalmichener"]
 if sp_base_version < parse_version("1.11"):  # pragma: no cover
     # Deprecated in SciPy 1.9 and removed in SciPy 1.11
     _VALID_METRICS += ["kulsinski"]
@@ -2482,10 +2484,12 @@ def pairwise_distances(
     "jaccard",
     "rogerstanimoto",
     "russellrao",
-    "sokalmichener",
     "sokalsneath",
     "yule",
 ]
+if sp_base_version < parse_version("1.17"):
+    # Deprecated in SciPy 1.15 and removed in SciPy 1.17
+    PAIRWISE_BOOLEAN_FUNCTIONS += ["sokalmichener"]
 if sp_base_version < parse_version("1.11"):
     # Deprecated in SciPy 1.9 and removed in SciPy 1.11
     PAIRWISE_BOOLEAN_FUNCTIONS += ["kulsinski"]
diff --git a/sklearn/metrics/tests/test_dist_metrics.py b/sklearn/metrics/tests/test_dist_metrics.py
index baaf447d3909b..5690274e27982 100644
--- a/sklearn/metrics/tests/test_dist_metrics.py
+++ b/sklearn/metrics/tests/test_dist_metrics.py
@@ -9,11 +9,16 @@
 from sklearn.metrics import DistanceMetric
 from sklearn.metrics._dist_metrics import (
     BOOL_METRICS,
+    DEPRECATED_METRICS,
     DistanceMetric32,
     DistanceMetric64,
 )
 from sklearn.utils import check_random_state
-from sklearn.utils._testing import assert_allclose, create_memmap_backed_data
+from sklearn.utils._testing import (
+    assert_allclose,
+    create_memmap_backed_data,
+    ignore_warnings,
+)
 from sklearn.utils.fixes import CSR_CONTAINERS, parse_version, sp_version
 
 
@@ -112,7 +117,15 @@ def test_cdist(metric_param_grid, X, Y, csr_container):
 )
 @pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
 def test_cdist_bool_metric(metric, X_bool, Y_bool, csr_container):
-    D_scipy_cdist = cdist(X_bool, Y_bool, metric)
+    if metric in DEPRECATED_METRICS:
+        with ignore_warnings(category=DeprecationWarning):
+            # Some metrics can be deprecated depending on the scipy version.
+            # But if they are present, we still want to test wether
+            # scikit-learn gives the same result, whether or not they are
+            # deprecated.
+            D_scipy_cdist = cdist(X_bool, Y_bool, metric)
+    else:
+        D_scipy_cdist = cdist(X_bool, Y_bool, metric)
 
     dm = DistanceMetric.get_metric(metric)
     D_sklearn = dm.pairwise(X_bool, Y_bool)
@@ -219,7 +232,16 @@ def test_distance_metrics_dtype_consistency(metric_param_grid):
 @pytest.mark.parametrize("X_bool", [X_bool, X_bool_mmap])
 @pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
 def test_pdist_bool_metrics(metric, X_bool, csr_container):
-    D_scipy_pdist = cdist(X_bool, X_bool, metric)
+    if metric in DEPRECATED_METRICS:
+        with ignore_warnings(category=DeprecationWarning):
+            # Some metrics can be deprecated depending on the scipy version.
+            # But if they are present, we still want to test wether
+            # scikit-learn gives the same result, whether or not they are
+            # deprecated.
+            D_scipy_pdist = cdist(X_bool, X_bool, metric)
+    else:
+        D_scipy_pdist = cdist(X_bool, X_bool, metric)
+
     dm = DistanceMetric.get_metric(metric)
     D_sklearn = dm.pairwise(X_bool)
     assert_allclose(D_sklearn, D_scipy_pdist)
diff --git a/sklearn/metrics/tests/test_pairwise.py b/sklearn/metrics/tests/test_pairwise.py
index b3f8146b275c5..f93dbcd6d8288 100644
--- a/sklearn/metrics/tests/test_pairwise.py
+++ b/sklearn/metrics/tests/test_pairwise.py
@@ -212,6 +212,9 @@ def test_pairwise_distances_for_sparse_data(
         pairwise_distances(X, Y_sparse, metric="minkowski")
 
 
+# Some scipy metrics are deprecated (depending on the scipy version) but we
+# still want to test them.
+@ignore_warnings(category=DeprecationWarning)
 @pytest.mark.parametrize("metric", PAIRWISE_BOOLEAN_FUNCTIONS)
 def test_pairwise_boolean_distance(metric):
     # test that we convert to boolean arrays for boolean distances
diff --git a/sklearn/neighbors/_base.py b/sklearn/neighbors/_base.py
index e8647d1a163a1..1925e0dbc758c 100644
--- a/sklearn/neighbors/_base.py
+++ b/sklearn/neighbors/_base.py
@@ -48,11 +48,13 @@
     "rogerstanimoto",
     "russellrao",
     "seuclidean",
-    "sokalmichener",
     "sokalsneath",
     "sqeuclidean",
     "yule",
 ]
+if sp_base_version < parse_version("1.17"):
+    # Deprecated in SciPy 1.15 and removed in SciPy 1.17
+    SCIPY_METRICS += ["sokalmichener"]
 if sp_base_version < parse_version("1.11"):
     # Deprecated in SciPy 1.9 and removed in SciPy 1.11
     SCIPY_METRICS += ["kulsinski"]
diff --git a/sklearn/neighbors/tests/test_neighbors.py b/sklearn/neighbors/tests/test_neighbors.py
index 1c434ae8d59d4..cb6acb65cb1cc 100644
--- a/sklearn/neighbors/tests/test_neighbors.py
+++ b/sklearn/neighbors/tests/test_neighbors.py
@@ -1721,6 +1721,10 @@ def test_neighbors_metrics(
             assert_array_equal(ball_tree_idx, kd_tree_idx)
 
 
+# TODO: Remove ignore_warnings when minimum supported SciPy version is 1.17
+# Some scipy metrics are deprecated (depending on the scipy version) but we
+# still want to test them.
+@ignore_warnings(category=DeprecationWarning)
 @pytest.mark.parametrize(
     "metric", sorted(set(neighbors.VALID_METRICS["brute"]) - set(["precomputed"]))
 )
@@ -2243,6 +2247,10 @@ def test_auto_algorithm(X, metric, metric_params, expected_algo):
     assert model._fit_method == expected_algo
 
 
+# TODO: Remove ignore_warnings when minimum supported SciPy version is 1.17
+# Some scipy metrics are deprecated (depending on the scipy version) but we
+# still want to test them.
+@ignore_warnings(category=DeprecationWarning)
 @pytest.mark.parametrize(
     "metric", sorted(set(neighbors.VALID_METRICS["brute"]) - set(["precomputed"]))
 )