diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 3dbee7d0929cb..986d6323e704e 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3397,7 +3397,10 @@ def _reindex_non_unique(self, target):
                 new_indexer = np.arange(len(self.take(indexer)))
                 new_indexer[~check] = -1
 
-        new_index = Index(new_labels, name=self.name)
+        if isinstance(self, ABCMultiIndex):
+            new_index = type(self).from_tuples(new_labels, names=self.names)
+        else:
+            new_index = Index(new_labels, name=self.name)
         return new_index, indexer, new_indexer
 
     # --------------------------------------------------------------------
diff --git a/pandas/tests/indexing/multiindex/test_loc.py b/pandas/tests/indexing/multiindex/test_loc.py
index f0cbdbe8d0564..63983f45d7832 100644
--- a/pandas/tests/indexing/multiindex/test_loc.py
+++ b/pandas/tests/indexing/multiindex/test_loc.py
@@ -491,3 +491,22 @@ def test_loc_datetime_mask_slicing():
         ),
     )
     tm.assert_series_equal(result, expected)
+
+
+def test_loc_with_mi_indexer():
+    # https://github.com/pandas-dev/pandas/issues/35351
+    df = DataFrame(
+        data=[["a", 1], ["a", 0], ["b", 1], ["c", 2]],
+        index=MultiIndex.from_tuples(
+            [(0, 1), (1, 0), (1, 1), (1, 1)], names=["index", "date"]
+        ),
+        columns=["author", "price"],
+    )
+    idx = MultiIndex.from_tuples([(0, 1), (1, 1)], names=["index", "date"])
+    result = df.loc[idx, :]
+    expected = DataFrame(
+        [["a", 1], ["b", 1], ["c", 2]],
+        index=MultiIndex.from_tuples([(0, 1), (1, 1), (1, 1)], names=["index", "date"]),
+        columns=["author", "price"],
+    )
+    tm.assert_frame_equal(result, expected)