diff --git a/pandas/_libs/tslibs/strptime.pyx b/pandas/_libs/tslibs/strptime.pyx
index ed784b6f5ab22..fb89f1328529d 100644
--- a/pandas/_libs/tslibs/strptime.pyx
+++ b/pandas/_libs/tslibs/strptime.pyx
@@ -924,6 +924,13 @@ cdef (int, int) _calc_julian_from_V(int iso_year, int iso_week, int iso_weekday)
 
     correction = date(iso_year, 1, 4).isoweekday() + 3
     ordinal = (iso_week * 7) + iso_weekday - correction
+
+    if iso_week == 53:
+        now = date.fromordinal(date(iso_year, 1, 1).toordinal() + ordinal - iso_weekday)
+        jan_4th = date(iso_year+1, 1, 4)
+        if (jan_4th - now).days < 7:
+            raise ValueError(f"Week 53 does not exist in ISO year {iso_year}.")
+
     # ordinal may be negative or 0 now, which means the date is in the previous
     # calendar year
     if ordinal < 1:
diff --git a/pandas/tests/tools/test_to_datetime.py b/pandas/tests/tools/test_to_datetime.py
index 566fd8d901569..e039f54960389 100644
--- a/pandas/tests/tools/test_to_datetime.py
+++ b/pandas/tests/tools/test_to_datetime.py
@@ -794,12 +794,36 @@ def test_to_datetime_np_str(self):
             ["2015-1-1", "%G-%V-%u", datetime(2014, 12, 29, 0, 0)],
             ["2015-1-4", "%G-%V-%u", datetime(2015, 1, 1, 0, 0)],
             ["2015-1-7", "%G-%V-%u", datetime(2015, 1, 4, 0, 0)],
+            ["2024-52-1", "%G-%V-%u", datetime(2024, 12, 23, 0, 0)],
+            ["2024-52-7", "%G-%V-%u", datetime(2024, 12, 29, 0, 0)],
+            ["2025-1-1", "%G-%V-%u", datetime(2024, 12, 30, 0, 0)],
+            ["2020-53-1", "%G-%V-%u", datetime(2020, 12, 28, 0, 0)],
         ],
     )
     def test_to_datetime_iso_week_year_format(self, s, _format, dt):
         # See GH#16607
         assert to_datetime(s, format=_format) == dt
 
+    @pytest.mark.parametrize(
+        "msg, s, _format",
+        [
+            [
+                "Week 53 does not exist in ISO year 2024",
+                "2024 53 1",
+                "%G %V %u",
+            ],
+            [
+                "Week 53 does not exist in ISO year 2023",
+                "2023 53 1",
+                "%G %V %u",
+            ],
+        ],
+    )
+    def test_invalid_iso_week_53(self, msg, s, _format):
+        # See GH#60885
+        with pytest.raises(ValueError, match=msg):
+            to_datetime(s, format=_format)
+
     @pytest.mark.parametrize(
         "msg, s, _format",
         [