diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index 635b1a1cd1326..235aa8e4aa922 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -1098,6 +1098,14 @@ def test_min_max_ordered(self, values, categories, function):
         expected = categories[0] if function == "min" else categories[2]
         assert result == expected
 
+    @pytest.mark.parametrize("function", ["min", "max"])
+    @pytest.mark.parametrize("skipna", [True, False])
+    def test_min_max_ordered_with_nan_only(self, function, skipna):
+        # https://github.com/pandas-dev/pandas/issues/33450
+        cat = Series(Categorical([np.nan], categories=[1, 2], ordered=True))
+        result = getattr(cat, function)(skipna=skipna)
+        assert result is np.nan
+
     @pytest.mark.parametrize("function", ["min", "max"])
     @pytest.mark.parametrize("skipna", [True, False])
     def test_min_max_skipna(self, function, skipna):