diff --git a/pandas/tests/groupby/test_missing.py b/pandas/tests/groupby/test_missing.py
index e53518269408a..f3149abb52291 100644
--- a/pandas/tests/groupby/test_missing.py
+++ b/pandas/tests/groupby/test_missing.py
@@ -43,6 +43,18 @@ def test_ffill_missing_arguments():
         df.groupby("b").fillna()
 
 
+@pytest.mark.parametrize(
+    "method, expected", [("ffill", [None, "a", "a"]), ("bfill", ["a", "a", None])]
+)
+def test_fillna_with_string_dtype(method, expected):
+    # GH 40250
+    df = DataFrame({"a": pd.array([None, "a", None], dtype="string"), "b": [0, 0, 0]})
+    grp = df.groupby("b")
+    result = grp.fillna(method=method)
+    expected = DataFrame({"a": pd.array(expected, dtype="string")})
+    tm.assert_frame_equal(result, expected)
+
+
 def test_fill_consistency():
 
     # GH9221