diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index b957ed4bab2..fb96ed6293c 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -44,6 +44,9 @@ Bug fixes
   :py:class:`CFTimeIndex` and upcoming pandas version 1.3.0 (:issue:`5356`,
   :pull:`5359`).
   By `Spencer Clark <https://github.com/spencerkclark>`_.
+- Fix 1-level multi-index incorrectly converted to single index (:issue:`5384`,
+  :pull:`5385`).
+  By `Benoit Bovy <https://github.com/benbovy>`_.
 
 
 Documentation
diff --git a/xarray/core/utils.py b/xarray/core/utils.py
index aa51366f588..3a9f418063d 100644
--- a/xarray/core/utils.py
+++ b/xarray/core/utils.py
@@ -107,6 +107,8 @@ def safe_cast_to_index(array: Any) -> pd.Index:
         index = array
     elif hasattr(array, "to_index"):
         index = array.to_index()
+    elif hasattr(array, "to_pandas_index"):
+        index = array.to_pandas_index()
     else:
         kwargs = {}
         if hasattr(array, "dtype") and array.dtype.kind == "O":
diff --git a/xarray/tests/test_utils.py b/xarray/tests/test_utils.py
index 8b5bcbedb7d..483fa723058 100644
--- a/xarray/tests/test_utils.py
+++ b/xarray/tests/test_utils.py
@@ -7,6 +7,7 @@
 
 from xarray.coding.cftimeindex import CFTimeIndex
 from xarray.core import duck_array_ops, utils
+from xarray.core.indexes import PandasIndex
 from xarray.core.utils import either_dict_or_kwargs
 
 from . import assert_array_equal, requires_cftime, requires_dask
@@ -28,11 +29,13 @@ def test_safe_cast_to_index():
     dates = pd.date_range("2000-01-01", periods=10)
     x = np.arange(5)
     td = x * np.timedelta64(1, "D")
+    midx = pd.MultiIndex.from_tuples([(0,)], names=["a"])
     for expected, array in [
         (dates, dates.values),
         (pd.Index(x, dtype=object), x.astype(object)),
         (pd.Index(td), td),
         (pd.Index(td, dtype=object), td.astype(object)),
+        (midx, PandasIndex(midx)),
     ]:
         actual = utils.safe_cast_to_index(array)
         assert_array_equal(expected, actual)