diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 54175fada6e56..e07a8fa0469f4 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -149,6 +149,8 @@ Indexing
 - Bug in slicing on a :class:`DatetimeIndex` with a partial-timestamp dropping high-resolution indices near the end of a year, quarter, or month (:issue:`31064`)
 - Bug in :meth:`PeriodIndex.get_loc` treating higher-resolution strings differently from :meth:`PeriodIndex.get_value` (:issue:`31172`)
 - Bug in :meth:`Series.at` and :meth:`DataFrame.at` not matching ``.loc`` behavior when looking up an integer in a :class:`Float64Index` (:issue:`31329`)
+- Bug in :meth:`PeriodIndex.is_monotonic` incorrectly returning ``True`` when containing leading ``NaT`` entries (:issue:`31437`)
+-
 
 Missing
 ^^^^^^^
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index 2dfc14378baf6..1915eaf6e07dd 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -514,8 +514,7 @@ cdef class PeriodEngine(Int64Engine):
         return super(PeriodEngine, self).vgetter().view("i8")
 
     cdef _call_monotonic(self, values):
-        # super(...) pattern doesn't seem to work with `cdef`
-        return Int64Engine._call_monotonic(self, values.view('i8'))
+        return algos.is_monotonic(values, timelike=True)
 
     def get_indexer(self, values):
         cdef:
diff --git a/pandas/tests/indexes/period/test_period.py b/pandas/tests/indexes/period/test_period.py
index 16fa0b0c25925..248df3291f040 100644
--- a/pandas/tests/indexes/period/test_period.py
+++ b/pandas/tests/indexes/period/test_period.py
@@ -662,3 +662,44 @@ def test_maybe_convert_timedelta():
     msg = r"Input has different freq=B from PeriodIndex\(freq=D\)"
     with pytest.raises(ValueError, match=msg):
         pi._maybe_convert_timedelta(offset)
+
+
+def test_is_monotonic_with_nat():
+    # GH#31437
+    # PeriodIndex.is_monotonic should behave analogously to DatetimeIndex,
+    #  in particular never be monotonic when we have NaT
+    dti = pd.date_range("2016-01-01", periods=3)
+    pi = dti.to_period("D")
+    tdi = pd.Index(dti.view("timedelta64[ns]"))
+
+    for obj in [pi, pi._engine, dti, dti._engine, tdi, tdi._engine]:
+        if isinstance(obj, pd.Index):
+            # i.e. not Engines
+            assert obj.is_monotonic
+        assert obj.is_monotonic_increasing
+        assert not obj.is_monotonic_decreasing
+        assert obj.is_unique
+
+    dti1 = dti.insert(0, pd.NaT)
+    pi1 = dti1.to_period("D")
+    tdi1 = pd.Index(dti1.view("timedelta64[ns]"))
+
+    for obj in [pi1, pi1._engine, dti1, dti1._engine, tdi1, tdi1._engine]:
+        if isinstance(obj, pd.Index):
+            # i.e. not Engines
+            assert not obj.is_monotonic
+        assert not obj.is_monotonic_increasing
+        assert not obj.is_monotonic_decreasing
+        assert obj.is_unique
+
+    dti2 = dti.insert(3, pd.NaT)
+    pi2 = dti2.to_period("H")
+    tdi2 = pd.Index(dti2.view("timedelta64[ns]"))
+
+    for obj in [pi2, pi2._engine, dti2, dti2._engine, tdi2, tdi2._engine]:
+        if isinstance(obj, pd.Index):
+            # i.e. not Engines
+            assert not obj.is_monotonic
+        assert not obj.is_monotonic_increasing
+        assert not obj.is_monotonic_decreasing
+        assert obj.is_unique
diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index 8d2058ffab643..0b312fe2f8990 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -440,7 +440,8 @@ def test_minmax_period(self):
 
         # monotonic
         idx1 = pd.PeriodIndex([NaT, "2011-01-01", "2011-01-02", "2011-01-03"], freq="D")
-        assert idx1.is_monotonic
+        assert not idx1.is_monotonic
+        assert idx1[1:].is_monotonic
 
         # non-monotonic
         idx2 = pd.PeriodIndex(