diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index 7450fc6fdc1da..57b2bf910e2e5 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -393,6 +393,7 @@ Datetimelike
 - Bug in :meth:`Timestamp.round` with values close to the implementation bounds returning incorrect results instead of raising ``OutOfBoundsDatetime`` (:issue:`51494`)
 - Bug in :meth:`arrays.DatetimeArray.map` and :meth:`DatetimeIndex.map`, where the supplied callable operated array-wise instead of element-wise (:issue:`51977`)
 - Bug in constructing a :class:`Series` or :class:`DataFrame` from a datetime or timedelta scalar always inferring nanosecond resolution instead of inferring from the input (:issue:`52212`)
+- Bug in constructing a :class:`Timestamp` from a string representing a time without a date inferring an incorrect unit (:issue:`54097`)
 - Bug in parsing datetime strings with weekday but no day e.g. "2023 Sept Thu" incorrectly raising ``AttributeError`` instead of ``ValueError`` (:issue:`52659`)
 
 Timedelta
diff --git a/pandas/_libs/tslibs/parsing.pyx b/pandas/_libs/tslibs/parsing.pyx
index 9173b7e8b1449..3643c840a50a6 100644
--- a/pandas/_libs/tslibs/parsing.pyx
+++ b/pandas/_libs/tslibs/parsing.pyx
@@ -42,10 +42,7 @@ cnp.import_array()
 
 from decimal import InvalidOperation
 
-from dateutil.parser import (
-    DEFAULTPARSER,
-    parse as du_parse,
-)
+from dateutil.parser import DEFAULTPARSER
 from dateutil.tz import (
     tzlocal as _dateutil_tzlocal,
     tzoffset,
@@ -309,9 +306,12 @@ cdef datetime parse_datetime_string(
         raise ValueError(f'Given date string "{date_string}" not likely a datetime')
 
     if _does_string_look_like_time(date_string):
+        # time without date e.g. "01:01:01.111"
         # use current datetime as default, not pass _DEFAULT_DATETIME
-        dt = du_parse(date_string, dayfirst=dayfirst,
-                      yearfirst=yearfirst)
+        default = datetime.now().replace(hour=0, minute=0, second=0, microsecond=0)
+        dt = dateutil_parse(date_string, default=default,
+                            dayfirst=dayfirst, yearfirst=yearfirst,
+                            ignoretz=False, out_bestunit=out_bestunit)
         return dt
 
     dt = _parse_delimited_date(date_string, dayfirst, out_bestunit)
diff --git a/pandas/tests/scalar/timestamp/test_constructors.py b/pandas/tests/scalar/timestamp/test_constructors.py
index 5fca577ff28d1..198b6feea5f4e 100644
--- a/pandas/tests/scalar/timestamp/test_constructors.py
+++ b/pandas/tests/scalar/timestamp/test_constructors.py
@@ -25,6 +25,11 @@
 
 
 class TestTimestampConstructors:
+    def test_construct_from_time_unit(self):
+        # GH#54097 only passing a time component, no date
+        ts = Timestamp("01:01:01.111")
+        assert ts.unit == "ms"
+
     def test_weekday_but_no_day_raises(self):
         # GH#52659
         msg = "Parsing datetimes with weekday but no day information is not supported"