diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index 3f898ca23bd6f..aff30d113438e 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -240,11 +240,10 @@ Styler
 
 Other
 ^^^^^
--
+- Bug in :func:`assert_almost_equal` now throwing assertion error for two unequal sets (:issue:`51727`)
 
 .. ***DO NOT USE THIS SECTION***
 
--
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/_libs/testing.pyx b/pandas/_libs/testing.pyx
index ca19670f37710..19aa4e173215e 100644
--- a/pandas/_libs/testing.pyx
+++ b/pandas/_libs/testing.pyx
@@ -95,6 +95,10 @@ cpdef assert_almost_equal(a, b,
     if robj is None:
         robj = b
 
+    if isinstance(a, set) or isinstance(b, set):
+        assert a == b, f"{a} != {b}"
+        return True
+
     if isinstance(a, dict) or isinstance(b, dict):
         return assert_dict_equal(a, b)
 
diff --git a/pandas/tests/util/test_assert_almost_equal.py b/pandas/tests/util/test_assert_almost_equal.py
index 0167e105efa23..5c50e5ad83967 100644
--- a/pandas/tests/util/test_assert_almost_equal.py
+++ b/pandas/tests/util/test_assert_almost_equal.py
@@ -202,6 +202,18 @@ def test_assert_almost_equal_edge_case_ndarrays(left_dtype, right_dtype):
     )
 
 
+def test_assert_almost_equal_sets():
+    # GH#51727
+    _assert_almost_equal_both({1, 2, 3}, {1, 2, 3})
+
+
+def test_assert_almost_not_equal_sets():
+    # GH#51727
+    msg = r"{1, 2, 3} != {1, 2, 4}"
+    with pytest.raises(AssertionError, match=msg):
+        _assert_almost_equal_both({1, 2, 3}, {1, 2, 4})
+
+
 def test_assert_almost_equal_dicts():
     _assert_almost_equal_both({"a": 1, "b": 2}, {"a": 1, "b": 2})
 
diff --git a/pandas/tests/util/test_assert_frame_equal.py b/pandas/tests/util/test_assert_frame_equal.py
index a6e29e243b0c8..2d3b47cd2e994 100644
--- a/pandas/tests/util/test_assert_frame_equal.py
+++ b/pandas/tests/util/test_assert_frame_equal.py
@@ -362,3 +362,20 @@ def test_assert_frame_equal_ts_column():
     msg = r'DataFrame.iloc\[:, 0\] \(column name="a"\) values are different'
     with pytest.raises(AssertionError, match=msg):
         tm.assert_frame_equal(df1, df2)
+
+
+def test_assert_frame_equal_set():
+    # GH#51727
+    df1 = DataFrame({"set_column": [{1, 2, 3}, {4, 5, 6}]})
+    df2 = DataFrame({"set_column": [{1, 2, 3}, {4, 5, 6}]})
+    tm.assert_frame_equal(df1, df2)
+
+
+def test_assert_frame_equal_set_mismatch():
+    # GH#51727
+    df1 = DataFrame({"set_column": [{1, 2, 3}, {4, 5, 6}]})
+    df2 = DataFrame({"set_column": [{1, 2, 3}, {4, 5, 7}]})
+
+    msg = r'DataFrame.iloc\[:, 0\] \(column name="set_column"\) values are different'
+    with pytest.raises(AssertionError, match=msg):
+        tm.assert_frame_equal(df1, df2)