diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 17cdb7538dad2..9c4de5c888299 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -619,6 +619,7 @@ Numeric
 - Bug in :class:`DataFrame` allowing arithmetic operations with list of array-likes with undefined results. Behavior changed to raising ``ValueError`` (:issue:`36702`)
 - Bug in :meth:`DataFrame.std` with ``timedelta64`` dtype and ``skipna=False`` (:issue:`37392`)
 - Bug in :meth:`DataFrame.min` and :meth:`DataFrame.max` with ``datetime64`` dtype and ``skipna=False`` (:issue:`36907`)
+- Bug in :meth:`DataFrame.idxmax` and :meth:`DataFrame.idxmin` with mixed dtypes incorrectly raising ``TypeError`` (:issue:`38195`)
 
 Conversion
 ^^^^^^^^^^
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 9cc9c9ef200cd..5f149f10b05d3 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -9001,7 +9001,11 @@ def idxmin(self, axis=0, skipna=True) -> Series:
         dtype: object
         """
         axis = self._get_axis_number(axis)
-        indices = nanops.nanargmin(self.values, axis=axis, skipna=skipna)
+
+        res = self._reduce(
+            nanops.nanargmin, "argmin", axis=axis, skipna=skipna, numeric_only=False
+        )
+        indices = res._values
 
         # indices will always be np.ndarray since axis is not None and
         # values is a 2d array for DataFrame
@@ -9074,7 +9078,11 @@ def idxmax(self, axis=0, skipna=True) -> Series:
         dtype: object
         """
         axis = self._get_axis_number(axis)
-        indices = nanops.nanargmax(self.values, axis=axis, skipna=skipna)
+
+        res = self._reduce(
+            nanops.nanargmax, "argmax", axis=axis, skipna=skipna, numeric_only=False
+        )
+        indices = res._values
 
         # indices will always be np.ndarray since axis is not None and
         # values is a 2d array for DataFrame
diff --git a/pandas/tests/frame/test_reductions.py b/pandas/tests/frame/test_reductions.py
index 299f00e818105..8cf1e17dfd1d0 100644
--- a/pandas/tests/frame/test_reductions.py
+++ b/pandas/tests/frame/test_reductions.py
@@ -969,6 +969,20 @@ def test_idxmax(self, float_frame, int_frame):
         with pytest.raises(ValueError, match=msg):
             frame.idxmax(axis=2)
 
+    def test_idxmax_mixed_dtype(self):
+        # don't cast to object, which would raise in nanops
+        dti = pd.date_range("2016-01-01", periods=3)
+
+        df = DataFrame({1: [0, 2, 1], 2: range(3)[::-1], 3: dti})
+
+        result = df.idxmax()
+        expected = Series([1, 0, 2], index=[1, 2, 3])
+        tm.assert_series_equal(result, expected)
+
+        result = df.idxmin()
+        expected = Series([0, 2, 0], index=[1, 2, 3])
+        tm.assert_series_equal(result, expected)
+
     # ----------------------------------------------------------------------
     # Logical reductions