diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 0ca19ffd1f496..d32eeb493b2c2 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -693,7 +693,6 @@ Other API changes
 - :func: `pandas.api.dtypes.is_string_dtype` no longer incorrectly identifies categorical series as string.
 - :func:`read_excel` no longer takes ``**kwds`` arguments. This means that passing in keyword ``chunksize`` now raises a ``TypeError``
   (previously raised a ``NotImplementedError``), while passing in keyword ``encoding`` now raises a ``TypeError`` (:issue:`34464`)
-- :func: `merge` now checks ``suffixes`` parameter type to be ``tuple`` and raises ``TypeError``, whereas before a ``list`` or ``set`` were accepted and that the ``set`` could produce unexpected results (:issue:`33740`)
 - :class:`Period` no longer accepts tuples for the ``freq`` argument (:issue:`34658`)
 - :meth:`Series.interpolate` and :meth:`DataFrame.interpolate` now raises ValueError if ``limit_direction`` is 'forward' or 'both' and ``method`` is 'backfill' or 'bfill' or ``limit_direction`` is 'backward' or 'both' and ``method`` is 'pad' or 'ffill' (:issue:`34746`)
 - The :class:`DataFrame` constructor no longer accepts a list of ``DataFrame`` objects. Because of changes to NumPy, ``DataFrame`` objects are now consistently treated as 2D objects, so a list of ``DataFrames`` is considered 3D, and no longer acceptible for the ``DataFrame`` constructor (:issue:`32289`).
@@ -787,6 +786,7 @@ Deprecations
 - :meth:`DataFrame.to_dict` has deprecated accepting short names for ``orient`` in future versions (:issue:`32515`)
 - :meth:`Categorical.to_dense` is deprecated and will be removed in a future version, use ``np.asarray(cat)`` instead (:issue:`32639`)
 - The ``fastpath`` keyword in the ``SingleBlockManager`` constructor is deprecated and will be removed in a future version (:issue:`33092`)
+- Providing ``suffixes`` as a ``set`` in :func:`pandas.merge` is deprecated. Provide a tuple instead (:issue:`33740`, :issue:`34741`).
 - :meth:`Index.is_mixed` is deprecated and will be removed in a future version, check ``index.inferred_type`` directly instead (:issue:`32922`)
 
 - Passing any arguments but the first one to  :func:`read_html` as
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index a21a45f415a47..b6993e9ed851a 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -227,10 +227,13 @@
 sort : bool, default False
     Sort the join keys lexicographically in the result DataFrame. If False,
     the order of the join keys depends on the join type (how keyword).
-suffixes : tuple of (str, str), default ('_x', '_y')
-    Suffix to apply to overlapping column names in the left and right
-    side, respectively. To raise an exception on overlapping columns use
-    (False, False).
+suffixes : list-like, default is ("_x", "_y")
+    A length-2 sequence where each element is optionally a string
+    indicating the suffix to add to overlapping column names in
+    `left` and `right` respectively. Pass a value of `None` instead
+    of a string to indicate that the column name from `left` or
+    `right` should be left as-is, with no suffix. At least one of the
+    values must not be None.
 copy : bool, default True
     If False, avoid copy if possible.
 indicator : bool or str, default False
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index 5e4eb89f0b45f..27b331babe692 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -194,7 +194,7 @@ def merge_ordered(
         left DataFrame.
     fill_method : {'ffill', None}, default None
         Interpolation method for data.
-    suffixes : Sequence, default is ("_x", "_y")
+    suffixes : list-like, default is ("_x", "_y")
         A length-2 sequence where each element is optionally a string
         indicating the suffix to add to overlapping column names in
         `left` and `right` respectively. Pass a value of `None` instead
@@ -2072,9 +2072,13 @@ def _items_overlap_with_suffix(left: Index, right: Index, suffixes: Tuple[str, s
     If corresponding suffix is empty, the entry is simply converted to string.
 
     """
-    if not isinstance(suffixes, tuple):
-        raise TypeError(
-            f"suffixes should be tuple of (str, str). But got {type(suffixes).__name__}"
+    if not is_list_like(suffixes, allow_sets=False):
+        warnings.warn(
+            f"Passing 'suffixes' as a {type(suffixes)}, is not supported and may give "
+            "unexpected results. Provide 'suffixes' as a tuple instead. In the "
+            "future a 'TypeError' will be raised.",
+            FutureWarning,
+            stacklevel=4,
         )
 
     to_rename = left.intersection(right)
diff --git a/pandas/tests/reshape/merge/test_merge.py b/pandas/tests/reshape/merge/test_merge.py
index 0a4d5f17a48cc..4fd3c688b8771 100644
--- a/pandas/tests/reshape/merge/test_merge.py
+++ b/pandas/tests/reshape/merge/test_merge.py
@@ -1999,6 +1999,7 @@ def test_merge_series(on, left_on, right_on, left_index, right_index, nm):
         (0, 0, dict(suffixes=("", "_dup")), ["0", "0_dup"]),
         (0, 0, dict(suffixes=(None, "_dup")), [0, "0_dup"]),
         (0, 0, dict(suffixes=("_x", "_y")), ["0_x", "0_y"]),
+        (0, 0, dict(suffixes=["_x", "_y"]), ["0_x", "0_y"]),
         ("a", 0, dict(suffixes=(None, "_y")), ["a", 0]),
         (0.0, 0.0, dict(suffixes=("_x", None)), ["0.0_x", 0.0]),
         ("b", "b", dict(suffixes=(None, "_y")), ["b", "b_y"]),
@@ -2069,18 +2070,13 @@ def test_merge_suffix_error(col1, col2, suffixes):
         pd.merge(a, b, left_index=True, right_index=True, suffixes=suffixes)
 
 
-@pytest.mark.parametrize(
-    "col1, col2, suffixes", [("a", "a", {"a", "b"}), ("a", "a", None), (0, 0, None)],
-)
-def test_merge_suffix_type_error(col1, col2, suffixes):
-    a = pd.DataFrame({col1: [1, 2, 3]})
-    b = pd.DataFrame({col2: [3, 4, 5]})
+@pytest.mark.parametrize("suffixes", [{"left", "right"}, {"left": 0, "right": 0}])
+def test_merge_suffix_warns(suffixes):
+    a = pd.DataFrame({"a": [1, 2, 3]})
+    b = pd.DataFrame({"b": [3, 4, 5]})
 
-    msg = (
-        f"suffixes should be tuple of \\(str, str\\). But got {type(suffixes).__name__}"
-    )
-    with pytest.raises(TypeError, match=msg):
-        pd.merge(a, b, left_index=True, right_index=True, suffixes=suffixes)
+    with tm.assert_produces_warning(FutureWarning):
+        pd.merge(a, b, left_index=True, right_index=True, suffixes={"left", "right"})
 
 
 @pytest.mark.parametrize(