diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 53c3f2e1c429a..e66b004e71ae5 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -2195,7 +2195,7 @@ def _reduce(self, name, axis=0, **kwargs):
         return func(**kwargs)
 
     @deprecate_kwarg(old_arg_name="numeric_only", new_arg_name="skipna")
-    def min(self, skipna=True, **kwargs):
+    def min(self, skipna=None, **kwargs):
         """
         The minimum value of the object.
 
@@ -2212,17 +2212,20 @@ def min(self, skipna=True, **kwargs):
         """
         self.check_for_ordered("min")
         good = self._codes != -1
-        if good.any():
+        if not good.all():
             if skipna:
                 pointer = self._codes[good].min(**kwargs)
             else:
+                msg = ("The default value of skipna will be changed to "
+                       "True in the future version.")
+                warn(msg, FutureWarning, stacklevel=2)
                 return np.nan
         else:
             pointer = self._codes.min(**kwargs)
         return self.categories[pointer]
 
     @deprecate_kwarg(old_arg_name="numeric_only", new_arg_name="skipna")
-    def max(self, skipna=True, **kwargs):
+    def max(self, skipna=None, **kwargs):
         """
         The maximum value of the object.
 
@@ -2239,10 +2242,13 @@ def max(self, skipna=True, **kwargs):
         """
         self.check_for_ordered("max")
         good = self._codes != -1
-        if good.any():
+        if not good.all():
             if skipna:
                 pointer = self._codes[good].max(**kwargs)
             else:
+                msg = ("The default value of skipna will be changed to "
+                       "True in the future version.")
+                warn(msg, FutureWarning, stacklevel=2)
                 return np.nan
         else:
             pointer = self._codes.max(**kwargs)
diff --git a/pandas/tests/arrays/categorical/test_analytics.py b/pandas/tests/arrays/categorical/test_analytics.py
index 72a7c5540b047..7e209626fe848 100644
--- a/pandas/tests/arrays/categorical/test_analytics.py
+++ b/pandas/tests/arrays/categorical/test_analytics.py
@@ -70,8 +70,9 @@ def test_deprecate_numeric_only_min_max(self, method):
         cat = Categorical(
             [np.nan, 1, 2, np.nan], categories=[5, 4, 3, 2, 1], ordered=True
         )
-        with tm.assert_produces_warning(expected_warning=FutureWarning):
-            getattr(cat, method)(numeric_only=False)
+        with tm.assert_produces_warning(expected_warning=FutureWarning,
+                                        check_stacklevel=False):
+            getattr(cat, method)(numeric_only=True)
 
     @pytest.mark.parametrize(
         "values,categories,exp_mode",