diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 25f847c698278..19e8acdaa7384 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -87,6 +87,7 @@ Other enhancements
 - Positional slicing on a :class:`IntervalIndex` now supports slices with ``step > 1`` (:issue:`31658`)
 - :class:`Series.str` now has a `fullmatch` method that matches a regular expression against the entire string in each row of the series, similar to `re.fullmatch` (:issue:`32806`).
 - :meth:`DataFrame.sample` will now also allow array-like and BitGenerator objects to be passed to ``random_state`` as seeds (:issue:`32503`)
+- :meth:`MultiIndex.union` will now raise `RuntimeWarning` if the object inside are unsortable, pass `sort=False` to suppress this warning (:issue:`33015`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/_libs/lib.pyx b/pandas/_libs/lib.pyx
index 6c6f6a8600ba2..6e7e8ff51f201 100644
--- a/pandas/_libs/lib.pyx
+++ b/pandas/_libs/lib.pyx
@@ -4,6 +4,7 @@ from fractions import Fraction
 from numbers import Number
 
 import sys
+import warnings
 
 import cython
 from cython import Py_ssize_t
@@ -286,7 +287,11 @@ def fast_unique_multiple(list arrays, sort: bool = True):
         try:
             uniques.sort()
         except TypeError:
-            # TODO: RuntimeWarning?
+            warnings.warn(
+                "The values in the array are unorderable. "
+                "Pass `sort=False` to suppress this warning.",
+                RuntimeWarning,
+            )
             pass
 
     return uniques
diff --git a/pandas/tests/indexes/multi/test_setops.py b/pandas/tests/indexes/multi/test_setops.py
index c97704e8a2066..d7427ee622977 100644
--- a/pandas/tests/indexes/multi/test_setops.py
+++ b/pandas/tests/indexes/multi/test_setops.py
@@ -337,7 +337,8 @@ def test_union_sort_other_incomparable():
     idx = pd.MultiIndex.from_product([[1, pd.Timestamp("2000")], ["a", "b"]])
 
     # default, sort=None
-    result = idx.union(idx[:1])
+    with tm.assert_produces_warning(RuntimeWarning):
+        result = idx.union(idx[:1])
     tm.assert_index_equal(result, idx)
 
     # sort=False
diff --git a/pandas/tests/test_lib.py b/pandas/tests/test_lib.py
index d914cf873de24..b6f59807eaa15 100644
--- a/pandas/tests/test_lib.py
+++ b/pandas/tests/test_lib.py
@@ -3,6 +3,7 @@
 
 from pandas._libs import lib, writers as libwriters
 
+import pandas as pd
 from pandas import Index
 import pandas._testing as tm
 
@@ -39,6 +40,11 @@ def test_fast_unique_multiple_list_gen_sort(self):
         out = lib.fast_unique_multiple_list_gen(gen, sort=False)
         tm.assert_numpy_array_equal(np.array(out), expected)
 
+    def test_fast_unique_multiple_unsortable_runtimewarning(self):
+        arr = [np.array(["foo", pd.Timestamp("2000")])]
+        with tm.assert_produces_warning(RuntimeWarning):
+            lib.fast_unique_multiple(arr, sort=None)
+
 
 class TestIndexing:
     def test_maybe_indices_to_slice_left_edge(self):