diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 690e6b8f725ad..57064bd348aa5 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -412,7 +412,7 @@ Timezones
 ^^^^^^^^^
 
 - Bug in :func:`date_range` was raising AmbiguousTimeError for valid input with ``ambiguous=False`` (:issue:`35297`)
--
+- Bug in :meth:`Timestamp.replace` was losing fold information (:issue:`37610`)
 
 
 Numeric
diff --git a/pandas/_libs/tslibs/nattype.pyx b/pandas/_libs/tslibs/nattype.pyx
index 88ad008b42c21..e10ac6a05ead8 100644
--- a/pandas/_libs/tslibs/nattype.pyx
+++ b/pandas/_libs/tslibs/nattype.pyx
@@ -774,7 +774,7 @@ default 'raise'
         microsecond : int, optional
         nanosecond : int, optional
         tzinfo : tz-convertible, optional
-        fold : int, optional, default is 0
+        fold : int, optional
 
         Returns
         -------
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index 9076325d01bab..b3ae69d7a3237 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -1374,7 +1374,7 @@ default 'raise'
         microsecond=None,
         nanosecond=None,
         tzinfo=object,
-        fold=0,
+        fold=None,
     ):
         """
         implements datetime.replace, handles nanoseconds.
@@ -1390,7 +1390,7 @@ default 'raise'
         microsecond : int, optional
         nanosecond : int, optional
         tzinfo : tz-convertible, optional
-        fold : int, optional, default is 0
+        fold : int, optional
 
         Returns
         -------
@@ -1407,6 +1407,11 @@ default 'raise'
         # set to naive if needed
         tzobj = self.tzinfo
         value = self.value
+
+        # GH 37610. Preserve fold when replacing.
+        if fold is None:
+            fold = self.fold
+
         if tzobj is not None:
             value = tz_convert_from_utc_single(value, tzobj)
 
diff --git a/pandas/tests/scalar/timestamp/test_unary_ops.py b/pandas/tests/scalar/timestamp/test_unary_ops.py
index e8196cd8328e7..88f99a6784ba1 100644
--- a/pandas/tests/scalar/timestamp/test_unary_ops.py
+++ b/pandas/tests/scalar/timestamp/test_unary_ops.py
@@ -424,3 +424,14 @@ def test_timestamp(self):
             # should agree with datetime.timestamp method
             dt = ts.to_pydatetime()
             assert dt.timestamp() == ts.timestamp()
+
+
+@pytest.mark.parametrize("fold", [0, 1])
+def test_replace_preserves_fold(fold):
+    # GH 37610. Check that replace preserves Timestamp fold property
+    tz = gettz("Europe/Moscow")
+
+    ts = Timestamp(year=2009, month=10, day=25, hour=2, minute=30, fold=fold, tzinfo=tz)
+    ts_replaced = ts.replace(second=1)
+
+    assert ts_replaced.fold == fold