diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 155cf21b4db..370394909e8 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -2262,6 +2262,8 @@ def _isel_fancy(
                     new_var = var.isel(indexers=var_indexers)
                 else:
                     new_var = var.copy(deep=False)
+                if name not in indexes:
+                    new_var = new_var.to_base_variable()
             variables[name] = new_var
 
         coord_names = self._coord_names & variables.keys()
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 96fa4ef144e..fe9ec56feea 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -1262,6 +1262,15 @@ def test_isel_dataarray(self):
         with pytest.raises(IndexError, match=r"dimension coordinate 'dim2'"):
             actual = data.isel(dim2=indexing_ds["dim2"])
 
+    def test_isel_fancy_convert_index_variable(self) -> None:
+        # select index variable "x" with a DataArray of dim "z"
+        # -> drop index and convert index variable to base variable
+        ds = xr.Dataset({"foo": ("x", [1, 2, 3])}, coords={"x": [0, 1, 2]})
+        idxr = xr.DataArray([1], dims="z", name="x")
+        actual = ds.isel(x=idxr)
+        assert "x" not in actual.xindexes
+        assert not isinstance(actual.x.variable, IndexVariable)
+
     def test_sel(self):
         data = create_test_data()
         int_slicers = {"dim1": slice(None, None, 2), "dim2": slice(2), "dim3": slice(3)}