diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 3a2a6c1dde7c8..9557eb616b833 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1085,6 +1085,12 @@ def _get_arithmetic_result_freq(self, other) -> BaseOffset | None:
             # e.g. TestTimedelta64ArithmeticUnsorted::test_timedelta
             # Day is unambiguously 24h
             return self.freq
+        elif (
+            lib.is_np_dtype(self.dtype, "M")
+            and isinstance(other, Timestamp)
+            and isinstance(self.freq, Day)
+        ):
+            return self.freq
 
         return None
 
diff --git a/pandas/tests/indexes/datetimes/test_arithmetic.py b/pandas/tests/indexes/datetimes/test_arithmetic.py
index ba9f82f1064ca..1c19133fff483 100644
--- a/pandas/tests/indexes/datetimes/test_arithmetic.py
+++ b/pandas/tests/indexes/datetimes/test_arithmetic.py
@@ -63,3 +63,14 @@ def test_add_dti_day(self):
         result = (dti + dti.freq)[:-1]
         expected = dti[1:]
         tm.assert_index_equal(result, expected)
+
+    def test_sub_timestamp_preserves_day_freq(self):
+        # GH#62094
+        dti = date_range("2021-01-01", periods=5, freq="D")
+        ts = Timestamp("2020-01-01")
+
+        result = dti - ts
+
+        # The one crucial assertion:
+        assert isinstance(result, TimedeltaIndex)
+        assert result.freq == dti.freq