diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 38b7a1d13c253..cbf0d4a4d708b 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -260,6 +260,7 @@ MultiIndex
 ^^^^^^^^^^
 
 - Bug in :meth:`DataFrame.drop` raising ``TypeError`` when :class:`MultiIndex` is non-unique and no level is provided (:issue:`36293`)
+- Bug in :meth:`MultiIndex.intersection` duplicating ``NaN`` in result (:issue:`38623`)
 - Bug in :meth:`MultiIndex.equals` incorrectly returning ``True`` when :class:`MultiIndex` containing ``NaN`` even when they are differntly ordered (:issue:`38439`)
 - Bug in :meth:`MultiIndex.intersection` always returning empty when intersecting with :class:`CategoricalIndex` (:issue:`38653`)
 
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 61b6b7ff19edc..f058645c4abda 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -3578,16 +3578,9 @@ def _intersection(self, other, sort=False):
                 uniq_tuples = algos.unique(inner_tuples)
 
         if uniq_tuples is None:
-            other_uniq = set(rvals)
-            seen = set()
-            # pandas\core\indexes\multi.py:3503: error: "add" of "set" does not
-            # return a value  [func-returns-value]
-            uniq_tuples = [
-                x
-                for x in lvals
-                if x in other_uniq
-                and not (x in seen or seen.add(x))  # type: ignore[func-returns-value]
-            ]
+            left_unique = self.drop_duplicates()
+            indexer = left_unique.get_indexer(other.drop_duplicates())
+            uniq_tuples = left_unique.take(np.sort(indexer[indexer != -1]))
 
         if sort is None:
             uniq_tuples = sorted(uniq_tuples)
diff --git a/pandas/tests/indexes/multi/test_setops.py b/pandas/tests/indexes/multi/test_setops.py
index d5b29527ee08e..f872315374174 100644
--- a/pandas/tests/indexes/multi/test_setops.py
+++ b/pandas/tests/indexes/multi/test_setops.py
@@ -483,3 +483,12 @@ def test_intersection_different_names():
     mi2 = MultiIndex.from_arrays([[1], [3]])
     result = mi.intersection(mi2)
     tm.assert_index_equal(result, mi2)
+
+
+def test_intersection_with_missing_values_on_both_sides(nulls_fixture):
+    # GH#38623
+    mi1 = MultiIndex.from_arrays([[3, nulls_fixture, 4, nulls_fixture], [1, 2, 4, 2]])
+    mi2 = MultiIndex.from_arrays([[3, nulls_fixture, 3], [1, 2, 4]])
+    result = mi1.intersection(mi2)
+    expected = MultiIndex.from_arrays([[3.0, nulls_fixture], [1, 2]])
+    tm.assert_index_equal(result, expected)