diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 8a7ad077c2a90..4590e2296f633 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -682,6 +682,8 @@ Other Deprecations
 - Deprecated the ``closed`` argument in :class:`IntervalArray` in favor of ``inclusive`` argument; In a future version passing ``closed`` will raise (:issue:`40245`)
 - Deprecated the ``closed`` argument in :class:`intervaltree` in favor of ``inclusive`` argument; In a future version passing ``closed`` will raise (:issue:`40245`)
 - Deprecated the ``closed`` argument in :class:`ArrowInterval` in favor of ``inclusive`` argument; In a future version passing ``closed`` will raise (:issue:`40245`)
+- Deprecated allowing ``unit="M"`` or ``unit="Y"`` in :class:`Timestamp` constructor with a non-round float value (:issue:`47267`)
+-
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_150.performance:
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index 808f750c18c9d..44335836dc2ee 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -1,5 +1,7 @@
 cimport cython
 
+import warnings
+
 import numpy as np
 
 cimport numpy as cnp
@@ -255,6 +257,18 @@ cdef _TSObject convert_to_tsobject(object ts, tzinfo tz, str unit,
         if ts != ts or ts == NPY_NAT:
             obj.value = NPY_NAT
         else:
+            if unit in ["Y", "M"]:
+                if ts != int(ts):
+                    # GH#47267 it is clear that 2 "M" corresponds to 1970-02-01,
+                    #  but not clear what 2.5 "M" corresponds to, so we will
+                    #  disallow that case.
+                    warnings.warn(
+                        "Conversion of non-round float with unit={unit} is ambiguous "
+                        "and will raise in a future version.",
+                        FutureWarning,
+                        stacklevel=1,
+                    )
+
             ts = cast_from_unit(ts, unit)
             obj.value = ts
             dt64_to_dtstruct(ts, &obj.dts)
diff --git a/pandas/tests/scalar/timestamp/test_constructors.py b/pandas/tests/scalar/timestamp/test_constructors.py
index a5641473c4d52..daf1730df489d 100644
--- a/pandas/tests/scalar/timestamp/test_constructors.py
+++ b/pandas/tests/scalar/timestamp/test_constructors.py
@@ -25,6 +25,15 @@
 
 
 class TestTimestampConstructors:
+    def test_constructor_float_not_round_with_YM_unit_deprecated(self):
+        # GH#47267 avoid the conversions in cast_from-unit
+
+        with tm.assert_produces_warning(FutureWarning, match="ambiguous"):
+            Timestamp(150.5, unit="Y")
+
+        with tm.assert_produces_warning(FutureWarning, match="ambiguous"):
+            Timestamp(150.5, unit="M")
+
     def test_constructor_datetime64_with_tz(self):
         # GH#42288, GH#24559
         dt = np.datetime64("1970-01-01 05:00:00")