diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 60364a87fd0..1c17075bbb7 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -97,6 +97,9 @@ Internal Changes
   By `Mathias Hauser <https://github.com/mathause>`_.
 - Ensure tests are not skipped in the `py38-all-but-dask` test environment
   (:issue:`4509`). By `Mathias Hauser <https://github.com/mathause>`_.
+- Replace the internal use of ``pd.Index.__or__`` and ``pd.Index.__and__`` with ``pd.Index.union``
+  and ``pd.Index.intersection`` as they will stop working as set operations in the future
+  (:issue:`4565`). By `Mathias Hauser <https://github.com/mathause>`_.
 
 .. _whats-new.0.16.1:
 
diff --git a/xarray/core/alignment.py b/xarray/core/alignment.py
index b42a5b2c7a9..21bda8ef8d7 100644
--- a/xarray/core/alignment.py
+++ b/xarray/core/alignment.py
@@ -32,9 +32,9 @@
 
 def _get_joiner(join):
     if join == "outer":
-        return functools.partial(functools.reduce, operator.or_)
+        return functools.partial(functools.reduce, pd.Index.union)
     elif join == "inner":
-        return functools.partial(functools.reduce, operator.and_)
+        return functools.partial(functools.reduce, pd.Index.intersection)
     elif join == "left":
         return operator.itemgetter(0)
     elif join == "right":