diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 705c335acfb48..cbc7159f55b8f 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -114,6 +114,7 @@ Datetimelike
 - :meth:`DatetimeArray.searchsorted`, :meth:`TimedeltaArray.searchsorted`, :meth:`PeriodArray.searchsorted` not recognizing non-pandas scalars and incorrectly raising ``ValueError`` instead of ``TypeError`` (:issue:`30950`)
 - Bug in :class:`Timestamp` where constructing :class:`Timestamp` with dateutil timezone less than 128 nanoseconds before daylight saving time switch from winter to summer would result in nonexistent time (:issue:`31043`)
 - Bug in :meth:`Period.to_timestamp`, :meth:`Period.start_time` with microsecond frequency returning a timestamp one nanosecond earlier than the correct time (:issue:`31475`)
+- :class:`Timestamp` raising confusing error message when year, month or day is missing (:issue:`31200`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index b8c462abe35f1..9f3b4a8a554b5 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -411,10 +411,25 @@ class Timestamp(_Timestamp):
                 )
 
         elif ts_input is _no_input:
-            # User passed keyword arguments.
-            ts_input = datetime(year, month, day, hour or 0,
-                                minute or 0, second or 0,
-                                microsecond or 0)
+            # GH 31200
+            # When year, month or day is not given, we call the datetime
+            # constructor to make sure we get the same error message
+            # since Timestamp inherits datetime
+            datetime_kwargs = {
+                "hour": hour or 0,
+                "minute": minute or 0,
+                "second": second or 0,
+                "microsecond": microsecond or 0
+            }
+            if year is not None:
+                datetime_kwargs["year"] = year
+            if month is not None:
+                datetime_kwargs["month"] = month
+            if day is not None:
+                datetime_kwargs["day"] = day
+
+            ts_input = datetime(**datetime_kwargs)
+
         elif is_integer_object(freq):
             # User passed positional arguments:
             # Timestamp(year, month, day[, hour[, minute[, second[,
diff --git a/pandas/tests/scalar/timestamp/test_constructors.py b/pandas/tests/scalar/timestamp/test_constructors.py
index b4a7173da84d0..4c75d1ebcd377 100644
--- a/pandas/tests/scalar/timestamp/test_constructors.py
+++ b/pandas/tests/scalar/timestamp/test_constructors.py
@@ -548,3 +548,16 @@ def test_timestamp_constructor_identity():
     expected = Timestamp("2017-01-01T12")
     result = Timestamp(expected)
     assert result is expected
+
+
+@pytest.mark.parametrize("kwargs", [{}, {"year": 2020}, {"year": 2020, "month": 1}])
+def test_constructor_missing_keyword(kwargs):
+    # GH 31200
+
+    # The exact error message of datetime() depends on its version
+    msg1 = r"function missing required argument '(year|month|day)' \(pos [123]\)"
+    msg2 = r"Required argument '(year|month|day)' \(pos [123]\) not found"
+    msg = "|".join([msg1, msg2])
+
+    with pytest.raises(TypeError, match=msg):
+        Timestamp(**kwargs)