diff --git a/pandas/tests/extension/base/missing.py b/pandas/tests/extension/base/missing.py
index cee565d4f7c1e..3a149025421b2 100644
--- a/pandas/tests/extension/base/missing.py
+++ b/pandas/tests/extension/base/missing.py
@@ -6,6 +6,8 @@
 
 
 class BaseMissingTests:
+    _supports_fillna_copy_false = True
+
     def test_isna(self, data_missing):
         expected = np.array([True, False])
 
@@ -179,3 +181,9 @@ def test_fillna_fill_other(self, data):
         expected = pd.DataFrame({"A": data, "B": [0.0] * len(result)})
 
         tm.assert_frame_equal(result, expected)
+
+    def test_fillna_readonly(self, data_missing):
+        fill_value = data_missing[1]
+        result = data_missing.fillna(fill_value, copy=False)
+        expected = data_missing.fillna(fill_value, copy=True)
+        tm.assert_extension_array_equal(result, expected)
diff --git a/pandas/tests/extension/test_numpy.py b/pandas/tests/extension/test_numpy.py
index 691ce9341b788..e19d1d7471ea6 100644
--- a/pandas/tests/extension/test_numpy.py
+++ b/pandas/tests/extension/test_numpy.py
@@ -167,6 +167,8 @@ def skip_numpy_object(dtype, request):
 
 
 class TestNumpyExtensionArray(base.ExtensionTests):
+    _supports_fillna_copy_false = False
+
     @pytest.mark.skip(reason="We don't register our dtype")
     # We don't want to register. This test should probably be split in two.
     def test_from_dtype(self, data):