diff --git a/xarray/core/indexes.py b/xarray/core/indexes.py
index 7de290f4e14..b42046e1706 100644
--- a/xarray/core/indexes.py
+++ b/xarray/core/indexes.py
@@ -1196,12 +1196,12 @@ def sel(self, labels, method=None, tolerance=None) -> IndexSelResult:
             coord_name, label = next(iter(labels.items()))
 
             if is_dict_like(label):
-                invalid_levels = [
+                invalid_levels = tuple(
                     name for name in label if name not in self.index.names
-                ]
+                )
                 if invalid_levels:
                     raise ValueError(
-                        f"invalid multi-index level names {invalid_levels}"
+                        f"multi-index level names {invalid_levels} not found in indexes {tuple(self.index.names)}"
                     )
                 return self.sel(label)
 
diff --git a/xarray/tests/test_indexes.py b/xarray/tests/test_indexes.py
index ebe9f3fb932..4ba849ea3ed 100644
--- a/xarray/tests/test_indexes.py
+++ b/xarray/tests/test_indexes.py
@@ -482,7 +482,10 @@ def test_sel(self) -> None:
             index.sel({"x": 0})
         with pytest.raises(ValueError, match=r"cannot provide labels for both.*"):
             index.sel({"one": 0, "x": "a"})
-        with pytest.raises(ValueError, match=r"invalid multi-index level names"):
+        with pytest.raises(
+            ValueError,
+            match=r"multi-index level names \('three',\) not found in indexes",
+        ):
             index.sel({"x": {"three": 0}})
         with pytest.raises(IndexError):
             index.sel({"x": (slice(None), 1, "no_level")})