diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 166ea2f0d4164..9859f12a34621 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -167,7 +167,7 @@ Missing
 
 MultiIndex
 ^^^^^^^^^^
--
+- Bug in :meth:`MultiIndex.reindex` when passing a ``level`` that corresponds to an ``ExtensionDtype`` level (:issue:`42043`)
 -
 
 I/O
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 02961bc98ec61..af5d704549c50 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -2503,9 +2503,7 @@ def reindex(
             target = ibase.ensure_has_len(target)
             if len(target) == 0 and not isinstance(target, Index):
                 idx = self.levels[level]
-                attrs = idx._get_attributes_dict()
-                attrs.pop("freq", None)  # don't preserve freq
-                target = type(idx)._simple_new(np.empty(0, dtype=idx.dtype), **attrs)
+                target = idx[:0]
             else:
                 target = ensure_index(target)
             target, indexer, _ = self._join_level(
diff --git a/pandas/tests/indexes/multi/test_reindex.py b/pandas/tests/indexes/multi/test_reindex.py
index 38ff6efec40c9..d9c77c5bdcd60 100644
--- a/pandas/tests/indexes/multi/test_reindex.py
+++ b/pandas/tests/indexes/multi/test_reindex.py
@@ -84,6 +84,13 @@ def test_reindex_lvl_preserves_type_if_target_is_empty_list_or_array():
     assert idx.reindex([], level=0)[0].levels[0].dtype.type == np.int64
     assert idx.reindex([], level=1)[0].levels[1].dtype.type == np.object_
 
+    # case with EA levels
+    cat = pd.Categorical(["foo", "bar"])
+    dti = pd.date_range("2016-01-01", periods=2, tz="US/Pacific")
+    mi = MultiIndex.from_product([cat, dti])
+    assert mi.reindex([], level=0)[0].levels[0].dtype == cat.dtype
+    assert mi.reindex([], level=1)[0].levels[1].dtype == dti.dtype
+
 
 def test_reindex_base(idx):
     idx = idx