diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 6b6010fa9c605..4032dc20b2e19 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -42,10 +42,7 @@ Other API Changes
 Deprecations
 ~~~~~~~~~~~~
 
--
--
--
-
+- Deprecated the `M (months)` and `Y (year)` `units` parameter of :func: `pandas.to_timedelta`, :func: `pandas.Timedelta` and :func: `pandas.TimedeltaIndex` (:issue:`16344`)
 
 .. _whatsnew_0250.prior_deprecations:
 
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 0a19d8749fc7c..f08a57375a301 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -1158,6 +1158,11 @@ class Timedelta(_Timedelta):
                                  "[weeks, days, hours, minutes, seconds, "
                                  "milliseconds, microseconds, nanoseconds]")
 
+        if unit in {'Y', 'y', 'M'}:
+            warnings.warn("M and Y units are deprecated and "
+                          "will be removed in a future version.",
+                          FutureWarning, stacklevel=1)
+
         if isinstance(value, Timedelta):
             value = value.value
         elif is_string_object(value):
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index cbe5ae198838f..830925535dab1 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -207,6 +207,11 @@ def __new__(cls, data=None, unit=None, freq=None, start=None, end=None,
                             'collection of some kind, {data} was passed'
                             .format(cls=cls.__name__, data=repr(data)))
 
+        if unit in {'Y', 'y', 'M'}:
+            warnings.warn("M and Y units are deprecated and "
+                          "will be removed in a future version.",
+                          FutureWarning, stacklevel=2)
+
         if isinstance(data, TimedeltaArray):
             if copy:
                 data = data.copy()
diff --git a/pandas/core/tools/timedeltas.py b/pandas/core/tools/timedeltas.py
index ddd21d0f62d08..30cb15f311b9f 100644
--- a/pandas/core/tools/timedeltas.py
+++ b/pandas/core/tools/timedeltas.py
@@ -2,6 +2,8 @@
 timedelta support tools
 """
 
+import warnings
+
 import numpy as np
 
 from pandas._libs.tslibs.timedeltas import Timedelta, parse_timedelta_unit
@@ -90,6 +92,11 @@ def to_timedelta(arg, unit='ns', box=True, errors='raise'):
         raise ValueError("errors must be one of 'ignore', "
                          "'raise', or 'coerce'}")
 
+    if unit in {'Y', 'y', 'M'}:
+        warnings.warn("M and Y units are deprecated and "
+                      "will be removed in a future version.",
+                      FutureWarning, stacklevel=2)
+
     if arg is None:
         return arg
     elif isinstance(arg, ABCSeries):
diff --git a/pandas/tests/indexes/timedeltas/test_timedelta.py b/pandas/tests/indexes/timedeltas/test_timedelta.py
index 79210705103ab..3cbd9942f9d84 100644
--- a/pandas/tests/indexes/timedeltas/test_timedelta.py
+++ b/pandas/tests/indexes/timedeltas/test_timedelta.py
@@ -1,4 +1,5 @@
 from datetime import timedelta
+import re
 
 import numpy as np
 import pytest
@@ -325,6 +326,13 @@ def test_freq_conversion(self):
         result = td.astype('timedelta64[s]')
         assert_index_equal(result, expected)
 
+    @pytest.mark.parametrize('unit', ['Y', 'y', 'M'])
+    def test_unit_m_y_deprecated(self, unit):
+        with tm.assert_produces_warning(FutureWarning) as w:
+            TimedeltaIndex([1, 3, 7], unit)
+        msg = r'.* units are deprecated .*'
+        assert re.match(msg, str(w[0].message))
+
 
 class TestTimeSeries(object):
 
diff --git a/pandas/tests/scalar/timedelta/test_timedelta.py b/pandas/tests/scalar/timedelta/test_timedelta.py
index e1838e0160fec..7d5b479810205 100644
--- a/pandas/tests/scalar/timedelta/test_timedelta.py
+++ b/pandas/tests/scalar/timedelta/test_timedelta.py
@@ -1,5 +1,6 @@
 """ test the scalar Timedelta """
 from datetime import timedelta
+import re
 
 import numpy as np
 import pytest
@@ -317,6 +318,7 @@ def test_nat_converters(self):
         assert result.dtype.kind == 'm'
         assert result.astype('int64') == iNaT
 
+    @pytest.mark.filterwarnings("ignore:M and Y units are deprecated")
     @pytest.mark.parametrize('units, np_unit',
                              [(['Y', 'y'], 'Y'),
                               (['M'], 'M'),
@@ -376,6 +378,24 @@ def test_unit_parser(self, units, np_unit, wrapper):
             result = Timedelta('2{}'.format(unit))
             assert result == expected
 
+    @pytest.mark.skipif(compat.PY2, reason="requires python3.5 or higher")
+    @pytest.mark.parametrize('unit', ['Y', 'y', 'M'])
+    def test_unit_m_y_deprecated(self, unit):
+        with tm.assert_produces_warning(FutureWarning) as w1:
+            Timedelta(10, unit)
+        msg = r'.* units are deprecated .*'
+        assert re.match(msg, str(w1[0].message))
+        with tm.assert_produces_warning(FutureWarning,
+                                        check_stacklevel=False) as w2:
+            to_timedelta(10, unit)
+        msg = r'.* units are deprecated .*'
+        assert re.match(msg, str(w2[0].message))
+        with tm.assert_produces_warning(FutureWarning,
+                                        check_stacklevel=False) as w3:
+            to_timedelta([1, 2], unit)
+        msg = r'.* units are deprecated .*'
+        assert re.match(msg, str(w3[0].message))
+
     def test_numeric_conversions(self):
         assert Timedelta(0) == np.timedelta64(0, 'ns')
         assert Timedelta(10) == np.timedelta64(10, 'ns')