diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index dfbbb456f50b6..7a1ccb3fa9ac3 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -194,6 +194,7 @@ Other enhancements
 - Added :meth:`Rolling.sem()` and :meth:`Expanding.sem()` to compute the standard error of mean (:issue:`26476`).
 - :meth:`Rolling.var()` and :meth:`Rolling.std()` use Kahan summation and Welfords Method to avoid numerical issues (:issue:`37051`)
 - :meth:`DataFrame.plot` now recognizes ``xlabel`` and ``ylabel`` arguments for plots of type ``scatter`` and ``hexbin`` (:issue:`37001`)
+- :class:`DataFrame` now supports ``divmod`` operation (:issue:`37165`)
 
 .. _whatsnew_120.api_breaking.python:
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index aca626805a0e3..a017ecf53c6ad 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5957,6 +5957,18 @@ def _construct_result(self, result) -> DataFrame:
         out.index = self.index
         return out
 
+    def __divmod__(self, other) -> Tuple[DataFrame, DataFrame]:
+        # Naive implementation, room for optimization
+        div = self // other
+        mod = self - div * other
+        return div, mod
+
+    def __rdivmod__(self, other) -> Tuple[DataFrame, DataFrame]:
+        # Naive implementation, room for optimization
+        div = other // self
+        mod = other - div * self
+        return div, mod
+
     # ----------------------------------------------------------------------
     # Combination-Related
 
diff --git a/pandas/tests/arithmetic/test_timedelta64.py b/pandas/tests/arithmetic/test_timedelta64.py
index 3e979aed0551f..90a3ed6d75393 100644
--- a/pandas/tests/arithmetic/test_timedelta64.py
+++ b/pandas/tests/arithmetic/test_timedelta64.py
@@ -1900,10 +1900,13 @@ def test_td64arr_mod_tdscalar(self, box_with_array, three_days):
         result = tdarr % three_days
         tm.assert_equal(result, expected)
 
-        if box_with_array is pd.DataFrame:
-            pytest.xfail("DataFrame does not have __divmod__ or __rdivmod__")
+        warn = None
+        if box_with_array is pd.DataFrame and isinstance(three_days, pd.DateOffset):
+            warn = PerformanceWarning
+
+        with tm.assert_produces_warning(warn):
+            result = divmod(tdarr, three_days)
 
-        result = divmod(tdarr, three_days)
         tm.assert_equal(result[1], expected)
         tm.assert_equal(result[0], tdarr // three_days)
 
@@ -1921,9 +1924,6 @@ def test_td64arr_mod_int(self, box_with_array):
         with pytest.raises(TypeError, match=msg):
             2 % tdarr
 
-        if box_with_array is pd.DataFrame:
-            pytest.xfail("DataFrame does not have __divmod__ or __rdivmod__")
-
         result = divmod(tdarr, 2)
         tm.assert_equal(result[1], expected)
         tm.assert_equal(result[0], tdarr // 2)
@@ -1939,9 +1939,6 @@ def test_td64arr_rmod_tdscalar(self, box_with_array, three_days):
         result = three_days % tdarr
         tm.assert_equal(result, expected)
 
-        if box_with_array is pd.DataFrame:
-            pytest.xfail("DataFrame does not have __divmod__ or __rdivmod__")
-
         result = divmod(three_days, tdarr)
         tm.assert_equal(result[1], expected)
         tm.assert_equal(result[0], three_days // tdarr)