diff --git a/xarray/core/groupby.py b/xarray/core/groupby.py
index 85ea0b5fddc..1bda5568c9a 100644
--- a/xarray/core/groupby.py
+++ b/xarray/core/groupby.py
@@ -236,6 +236,10 @@ def __getitem__(self, key):
             key = key[0]
         return self.values[key]
 
+    def to_index(self) -> pd.Index:
+        # could be pd.RangeIndex?
+        return pd.Index(np.arange(self.size))
+
     def copy(self, deep: bool = True, data: Any = None):
         raise NotImplementedError
 
@@ -381,7 +385,7 @@ def is_unique_and_monotonic(self) -> bool:
     @property
     def group_as_index(self) -> pd.Index:
         if self._group_as_index is None:
-            self._group_as_index = safe_cast_to_index(self.group1d)
+            self._group_as_index = self.group1d.to_index()
         return self._group_as_index
 
 
diff --git a/xarray/tests/test_groupby.py b/xarray/tests/test_groupby.py
index 97ba0b585e8..8a93cf930a5 100644
--- a/xarray/tests/test_groupby.py
+++ b/xarray/tests/test_groupby.py
@@ -2340,6 +2340,14 @@ def test_groupby_binary_op_regression() -> None:
     assert_identical(xr.zeros_like(anom_gb), anom_gb)
 
 
+def test_groupby_multiindex_level() -> None:
+    # GH6836
+    midx = pd.MultiIndex.from_product([list("abc"), [0, 1]], names=("one", "two"))
+    mda = xr.DataArray(np.random.rand(6, 3), [("x", midx), ("y", range(3))])
+    groups = mda.groupby("one").groups
+    assert groups == {"a": [0, 1], "b": [2, 3], "c": [4, 5]}
+
+
 @requires_flox
 @pytest.mark.parametrize("func", ["sum", "prod"])
 @pytest.mark.parametrize("skipna", [True, False])