diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index dd63ea94d5211..a576e0090747a 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -2226,9 +2226,12 @@ def append(self, other):
 
     def argsort(self, *args, **kwargs) -> npt.NDArray[np.intp]:
         if len(args) == 0 and len(kwargs) == 0:
-            # np.lexsort is significantly faster than self._values.argsort()
-            values = [self._get_level_values(i) for i in reversed(range(self.nlevels))]
-            return np.lexsort(values)
+            if not any(-1 in code for code in self.codes):
+                # np.lexsort is significantly faster than self._values.argsort()
+                values = [
+                    self._get_level_values(i) for i in reversed(range(self.nlevels))
+                ]
+                return np.lexsort(values)
         return self._values.argsort(*args, **kwargs)
 
     @Appender(_index_shared_docs["repeat"] % _index_doc_kwargs)
diff --git a/pandas/tests/indexes/multi/test_sorting.py b/pandas/tests/indexes/multi/test_sorting.py
index 6fd1781beeda4..0512daae694ce 100644
--- a/pandas/tests/indexes/multi/test_sorting.py
+++ b/pandas/tests/indexes/multi/test_sorting.py
@@ -280,3 +280,13 @@ def test_remove_unused_levels_with_nan():
     result = idx.levels
     expected = FrozenList([["a", np.nan], [4]])
     assert str(result) == str(expected)
+
+
+def test_sort_values_nan():
+    # GH#
+    midx = MultiIndex(levels=[["A", "B", "C"], ["D"]], codes=[[1, 0, 2], [-1, -1, 0]])
+    result = midx.sort_values()
+    expected = MultiIndex(
+        levels=[["A", "B", "C"], ["D"]], codes=[[0, 1, 2], [-1, -1, 0]]
+    )
+    tm.assert_index_equal(result, expected)