diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index d8961f5fdb959..874caee23dae6 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -394,6 +394,7 @@ Numeric
 - Bug in :meth:`DataFrame.__rmatmul__` error handling reporting transposed shapes (:issue:`21581`)
 - Bug in :class:`Series` flex arithmetic methods where the result when operating with a ``list``, ``tuple`` or ``np.ndarray`` would have an incorrect name (:issue:`36760`)
 - Bug in :class:`IntegerArray` multiplication with ``timedelta`` and ``np.timedelta64`` objects (:issue:`36870`)
+- Bug in :class:`MultiIndex` comparison with tuple incorrectly treating tuple as array-like (:issue:`21517`)
 - Bug in :meth:`DataFrame.diff` with ``datetime64`` dtypes including ``NaT`` values failing to fill ``NaT`` results correctly (:issue:`32441`)
 - Bug in :class:`DataFrame` arithmetic ops incorrectly accepting keyword arguments (:issue:`36843`)
 - Bug in :class:`IntervalArray` comparisons with :class:`Series` not returning :class:`Series` (:issue:`36908`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 2ebf2389823e9..3713eb6da60ac 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -65,7 +65,6 @@
 )
 from pandas.core.dtypes.concat import concat_compat
 from pandas.core.dtypes.generic import (
-    ABCCategorical,
     ABCDatetimeIndex,
     ABCMultiIndex,
     ABCPandasArray,
@@ -83,6 +82,7 @@
 from pandas.core.arrays.datetimes import tz_to_dtype, validate_tz_from_dtype
 from pandas.core.base import IndexOpsMixin, PandasObject
 import pandas.core.common as com
+from pandas.core.construction import extract_array
 from pandas.core.indexers import deprecate_ndim_indexing
 from pandas.core.indexes.frozen import FrozenList
 from pandas.core.ops import get_op_result_name
@@ -5376,11 +5376,13 @@ def _cmp_method(self, other, op):
             if len(self) != len(other):
                 raise ValueError("Lengths must match to compare")
 
-        if is_object_dtype(self.dtype) and isinstance(other, ABCCategorical):
-            left = type(other)(self._values, dtype=other.dtype)
-            return op(left, other)
-        elif is_object_dtype(self.dtype) and isinstance(other, ExtensionArray):
-            # e.g. PeriodArray
+        if not isinstance(other, ABCMultiIndex):
+            other = extract_array(other, extract_numpy=True)
+        else:
+            other = np.asarray(other)
+
+        if is_object_dtype(self.dtype) and isinstance(other, ExtensionArray):
+            # e.g. PeriodArray, Categorical
             with np.errstate(all="ignore"):
                 result = op(self._values, other)
 
@@ -5395,7 +5397,7 @@ def _cmp_method(self, other, op):
 
         else:
             with np.errstate(all="ignore"):
-                result = ops.comparison_op(self._values, np.asarray(other), op)
+                result = ops.comparison_op(self._values, other, op)
 
         return result
 
diff --git a/pandas/tests/indexes/multi/test_equivalence.py b/pandas/tests/indexes/multi/test_equivalence.py
index 184cedea7dc5c..fec1c0e44cd9f 100644
--- a/pandas/tests/indexes/multi/test_equivalence.py
+++ b/pandas/tests/indexes/multi/test_equivalence.py
@@ -84,6 +84,46 @@ def test_equals_op(idx):
         tm.assert_series_equal(series_a == item, Series(expected3))
 
 
+def test_compare_tuple():
+    # GH#21517
+    mi = MultiIndex.from_product([[1, 2]] * 2)
+
+    all_false = np.array([False, False, False, False])
+
+    result = mi == mi[0]
+    expected = np.array([True, False, False, False])
+    tm.assert_numpy_array_equal(result, expected)
+
+    result = mi != mi[0]
+    tm.assert_numpy_array_equal(result, ~expected)
+
+    result = mi < mi[0]
+    tm.assert_numpy_array_equal(result, all_false)
+
+    result = mi <= mi[0]
+    tm.assert_numpy_array_equal(result, expected)
+
+    result = mi > mi[0]
+    tm.assert_numpy_array_equal(result, ~expected)
+
+    result = mi >= mi[0]
+    tm.assert_numpy_array_equal(result, ~all_false)
+
+
+def test_compare_tuple_strs():
+    # GH#34180
+
+    mi = MultiIndex.from_tuples([("a", "b"), ("b", "c"), ("c", "a")])
+
+    result = mi == ("c", "a")
+    expected = np.array([False, False, True])
+    tm.assert_numpy_array_equal(result, expected)
+
+    result = mi == ("c",)
+    expected = np.array([False, False, False])
+    tm.assert_numpy_array_equal(result, expected)
+
+
 def test_equals_multi(idx):
     assert idx.equals(idx)
     assert not idx.equals(idx.values)