diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 62e508c491740..5353969d9a556 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -1956,6 +1956,7 @@ def min(self, *, skipna=True, **kwargs):
         -------
         min : the minimum of this `Categorical`
         """
+        nv.validate_minmax_axis(kwargs.get("axis", 0))
         nv.validate_min((), kwargs)
         self.check_for_ordered("min")
 
@@ -1992,6 +1993,7 @@ def max(self, *, skipna=True, **kwargs):
         -------
         max : the maximum of this `Categorical`
         """
+        nv.validate_minmax_axis(kwargs.get("axis", 0))
         nv.validate_max((), kwargs)
         self.check_for_ordered("max")
 
diff --git a/pandas/tests/arrays/categorical/test_analytics.py b/pandas/tests/arrays/categorical/test_analytics.py
index 7bd7d29ec9703..abf4ddd681d69 100644
--- a/pandas/tests/arrays/categorical/test_analytics.py
+++ b/pandas/tests/arrays/categorical/test_analytics.py
@@ -113,6 +113,8 @@ def test_numpy_min_max_unsupported_kwargs_raises(self, method, kwarg):
             f"the '{kwarg}' parameter is not supported in the pandas implementation "
             f"of {method}"
         )
+        if kwarg == "axis":
+            msg = r"`axis` must be fewer than the number of dimensions \(1\)"
         kwargs = {kwarg: 42}
         method = getattr(np, method)
         with pytest.raises(ValueError, match=msg):
diff --git a/pandas/tests/indexes/datetimelike.py b/pandas/tests/indexes/datetimelike.py
index 7ce8640d09777..14f9c2f9de284 100644
--- a/pandas/tests/indexes/datetimelike.py
+++ b/pandas/tests/indexes/datetimelike.py
@@ -10,19 +10,6 @@
 
 
 class DatetimeLike(Base):
-    def test_argmax_axis_invalid(self):
-        # GH#23081
-        msg = r"`axis` must be fewer than the number of dimensions \(1\)"
-        rng = self.create_index()
-        with pytest.raises(ValueError, match=msg):
-            rng.argmax(axis=1)
-        with pytest.raises(ValueError, match=msg):
-            rng.argmin(axis=2)
-        with pytest.raises(ValueError, match=msg):
-            rng.min(axis=-2)
-        with pytest.raises(ValueError, match=msg):
-            rng.max(axis=-3)
-
     def test_can_hold_identifiers(self):
         idx = self.create_index()
         key = idx[0]
diff --git a/pandas/tests/indexes/test_any_index.py b/pandas/tests/indexes/test_any_index.py
index 5e7065f785309..afeeb63217489 100644
--- a/pandas/tests/indexes/test_any_index.py
+++ b/pandas/tests/indexes/test_any_index.py
@@ -89,3 +89,17 @@ def test_str(self, index):
         index.name = "foo"
         assert "'foo'" in str(index)
         assert type(index).__name__ in str(index)
+
+
+class TestReductions:
+    def test_argmax_axis_invalid(self, index):
+        # GH#23081
+        msg = r"`axis` must be fewer than the number of dimensions \(1\)"
+        with pytest.raises(ValueError, match=msg):
+            index.argmax(axis=1)
+        with pytest.raises(ValueError, match=msg):
+            index.argmin(axis=2)
+        with pytest.raises(ValueError, match=msg):
+            index.min(axis=-2)
+        with pytest.raises(ValueError, match=msg):
+            index.max(axis=-3)