diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index 4682d262bf300..ea4bb42fb7ee1 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -2873,3 +2873,21 @@ def test_obj_with_exclusions_duplicate_columns():
     result = gb._obj_with_exclusions
     expected = df.take([0, 2, 3], axis=1)
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize("numeric_only", [True, False])
+def test_groupby_numeric_only_std_no_result(numeric_only):
+    # GH 51080
+    dicts_non_numeric = [{"a": "foo", "b": "bar"}, {"a": "car", "b": "dar"}]
+    df = DataFrame(dicts_non_numeric)
+    dfgb = df.groupby("a", as_index=False, sort=False)
+
+    if numeric_only:
+        result = dfgb.std(numeric_only=True)
+        expected_df = DataFrame(["foo", "car"], columns=["a"])
+        tm.assert_frame_equal(result, expected_df)
+    else:
+        with pytest.raises(
+            ValueError, match="could not convert string to float: 'bar'"
+        ):
+            dfgb.std(numeric_only=numeric_only)