diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index cf3dd1b0e3226..6b59349ce52b2 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -790,6 +790,7 @@ Indexing
 - Bug in :meth:`DataFrame.loc.__setitem__` when setting-with-expansion incorrectly raising when the index in the expanding axis contains duplicates (:issue:`40096`)
 - Bug in :meth:`DataFrame.loc` incorrectly matching non-boolean index elements (:issue:`20432`)
 - Bug in :meth:`Series.__delitem__` with ``ExtensionDtype`` incorrectly casting to ``ndarray`` (:issue:`40386`)
+- Bug in :meth:`DataFrame.__setitem__` raising ``TypeError`` when using a str subclass as the column name with a :class:`DatetimeIndex` (:issue:`37366`)
 
 Missing
 ^^^^^^^
diff --git a/pandas/core/indexing.py b/pandas/core/indexing.py
index 96aeda955df01..2f8919644486b 100644
--- a/pandas/core/indexing.py
+++ b/pandas/core/indexing.py
@@ -2289,7 +2289,7 @@ def convert_to_index_sliceable(obj: DataFrame, key):
         # slice here via partial string indexing
         if idx._supports_partial_string_indexing:
             try:
-                res = idx._get_string_slice(key)
+                res = idx._get_string_slice(str(key))
                 warnings.warn(
                     "Indexing a DataFrame with a datetimelike index using a single "
                     "string to slice the rows, like `frame[string]`, is deprecated "
diff --git a/pandas/tests/indexing/test_datetime.py b/pandas/tests/indexing/test_datetime.py
index 29a037c1d3b52..e46eed05caa86 100644
--- a/pandas/tests/indexing/test_datetime.py
+++ b/pandas/tests/indexing/test_datetime.py
@@ -152,3 +152,16 @@ def test_getitem_millisecond_resolution(self, frame_or_series):
             ],
         )
         tm.assert_equal(result, expected)
+
+    def test_str_subclass(self):
+        # GH 37366
+        class mystring(str):
+            pass
+
+        data = ["2020-10-22 01:21:00+00:00"]
+        index = pd.DatetimeIndex(data)
+        df = DataFrame({"a": [1]}, index=index)
+        df["b"] = 2
+        df[mystring("c")] = 3
+        expected = DataFrame({"a": [1], "b": [2], mystring("c"): [3]}, index=index)
+        tm.assert_equal(df, expected)