diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index b4c00b66ed8..10bf1466156 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -5867,7 +5867,7 @@ def drop_vars(
         for var in names_set:
             maybe_midx = self._indexes.get(var, None)
             if isinstance(maybe_midx, PandasMultiIndex):
-                idx_coord_names = set(maybe_midx.index.names + [maybe_midx.dim])
+                idx_coord_names = set(list(maybe_midx.index.names) + [maybe_midx.dim])
                 idx_other_names = idx_coord_names - set(names_set)
                 other_names.update(idx_other_names)
         if other_names:
diff --git a/xarray/tests/test_indexes.py b/xarray/tests/test_indexes.py
index 3ee7f045360..5ebdfd5da6e 100644
--- a/xarray/tests/test_indexes.py
+++ b/xarray/tests/test_indexes.py
@@ -352,7 +352,7 @@ def test_constructor(self) -> None:
         # default level names
         pd_idx = pd.MultiIndex.from_arrays([foo_data, bar_data])
         index = PandasMultiIndex(pd_idx, "x")
-        assert index.index.names == ("x_level_0", "x_level_1")
+        assert list(index.index.names) == ["x_level_0", "x_level_1"]
 
     def test_from_variables(self) -> None:
         v_level1 = xr.Variable(
@@ -370,7 +370,7 @@ def test_from_variables(self) -> None:
         assert index.dim == "x"
         assert index.index.equals(expected_idx)
         assert index.index.name == "x"
-        assert index.index.names == ["level1", "level2"]
+        assert list(index.index.names) == ["level1", "level2"]
 
         var = xr.Variable(("x", "y"), [[1, 2, 3], [4, 5, 6]])
         with pytest.raises(
@@ -413,7 +413,8 @@ def test_stack(self) -> None:
         index = PandasMultiIndex.stack(prod_vars, "z")
 
         assert index.dim == "z"
-        assert index.index.names == ["x", "y"]
+        # TODO: change to tuple when pandas 3 is minimum
+        assert list(index.index.names) == ["x", "y"]
         np.testing.assert_array_equal(
             index.index.codes, [[0, 0, 0, 1, 1, 1], [0, 1, 2, 0, 1, 2]]
         )
@@ -531,12 +532,12 @@ def test_rename(self) -> None:
         assert new_index is index
 
         new_index = index.rename({"two": "three"}, {})
-        assert new_index.index.names == ["one", "three"]
+        assert list(new_index.index.names) == ["one", "three"]
         assert new_index.dim == "x"
         assert new_index.level_coords_dtype == {"one": "<U1", "three": np.int32}
 
         new_index = index.rename({}, {"x": "y"})
-        assert new_index.index.names == ["one", "two"]
+        assert list(new_index.index.names) == ["one", "two"]
         assert new_index.dim == "y"
         assert new_index.level_coords_dtype == level_coords_dtype