diff --git a/doc/source/whatsnew/v0.20.3.txt b/doc/source/whatsnew/v0.20.3.txt
index 3d6aba98d4d57..c11c74211030a 100644
--- a/doc/source/whatsnew/v0.20.3.txt
+++ b/doc/source/whatsnew/v0.20.3.txt
@@ -83,7 +83,7 @@ Sparse
 
 Reshaping
 ^^^^^^^^^
-
+- ``PeriodIndex`` / ``TimedeltaIndex.join`` was missing the ``sort=`` kwarg (:issue:`16541`) 
 - Bug in joining on a ``MultiIndex`` with a ``category`` dtype for a level (:issue:`16627`).
 - Bug in :func:`merge` when merging/joining with multiple categorical columns (:issue:`16767`)
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 8a4878d9cfbcf..cefb080a3ee78 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3126,7 +3126,7 @@ def _join_non_unique(self, other, how='left', return_indexers=False):
         left_idx = _ensure_platform_int(left_idx)
         right_idx = _ensure_platform_int(right_idx)
 
-        join_index = self.values.take(left_idx)
+        join_index = np.asarray(self.values.take(left_idx))
         mask = left_idx == -1
         np.putmask(join_index, mask, other._values.take(right_idx))
 
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 9d1a49e13c804..0915462d4d421 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -912,14 +912,16 @@ def insert(self, loc, item):
                               self[loc:].asi8))
         return self._shallow_copy(idx)
 
-    def join(self, other, how='left', level=None, return_indexers=False):
+    def join(self, other, how='left', level=None, return_indexers=False,
+             sort=False):
         """
         See Index.join
         """
         self._assert_can_do_setop(other)
 
         result = Int64Index.join(self, other, how=how, level=level,
-                                 return_indexers=return_indexers)
+                                 return_indexers=return_indexers,
+                                 sort=sort)
 
         if return_indexers:
             result, lidx, ridx = result
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index c025c74625972..faec813df3993 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -516,7 +516,8 @@ def union(self, other):
                     result.freq = to_offset(result.inferred_freq)
             return result
 
-    def join(self, other, how='left', level=None, return_indexers=False):
+    def join(self, other, how='left', level=None, return_indexers=False,
+             sort=False):
         """
         See Index.join
         """
@@ -527,7 +528,8 @@ def join(self, other, how='left', level=None, return_indexers=False):
                 pass
 
         return Index.join(self, other, how=how, level=level,
-                          return_indexers=return_indexers)
+                          return_indexers=return_indexers,
+                          sort=sort)
 
     def _wrap_joined_index(self, joined, other):
         name = self.name if self.name == other.name else None
diff --git a/pandas/tests/frame/test_join.py b/pandas/tests/frame/test_join.py
index 21807cb42aa6e..afecba2026dd7 100644
--- a/pandas/tests/frame/test_join.py
+++ b/pandas/tests/frame/test_join.py
@@ -3,11 +3,19 @@
 import pytest
 import numpy as np
 
-from pandas import DataFrame, Index
+from pandas import DataFrame, Index, PeriodIndex
 from pandas.tests.frame.common import TestData
 import pandas.util.testing as tm
 
 
+@pytest.fixture
+def frame_with_period_index():
+    return DataFrame(
+        data=np.arange(20).reshape(4, 5),
+        columns=list('abcde'),
+        index=PeriodIndex(start='2000', freq='A', periods=4))
+
+
 @pytest.fixture
 def frame():
     return TestData().frame
@@ -139,3 +147,21 @@ def test_join_overlap(frame):
 
     # column order not necessarily sorted
     tm.assert_frame_equal(joined, expected.loc[:, joined.columns])
+
+
+def test_join_period_index(frame_with_period_index):
+    other = frame_with_period_index.rename(
+        columns=lambda x: '{key}{key}'.format(key=x))
+
+    joined_values = np.concatenate(
+        [frame_with_period_index.values] * 2, axis=1)
+
+    joined_cols = frame_with_period_index.columns.append(other.columns)
+
+    joined = frame_with_period_index.join(other)
+    expected = DataFrame(
+        data=joined_values,
+        columns=joined_cols,
+        index=frame_with_period_index.index)
+
+    tm.assert_frame_equal(joined, expected)
diff --git a/pandas/tests/indexes/common.py b/pandas/tests/indexes/common.py
index a6177104d6273..e7ca435dca1c1 100644
--- a/pandas/tests/indexes/common.py
+++ b/pandas/tests/indexes/common.py
@@ -905,7 +905,7 @@ def test_fillna(self):
 
     def test_nulls(self):
         # this is really a smoke test for the methods
-        # as these are adequantely tested for function elsewhere
+        # as these are adequately tested for function elsewhere
 
         for name, index in self.indices.items():
             if len(index) == 0:
@@ -933,3 +933,10 @@ def test_empty(self):
         index = self.create_index()
         assert not index.empty
         assert index[:0].empty
+
+    @pytest.mark.parametrize('how', ['outer', 'inner', 'left', 'right'])
+    def test_join_self_unique(self, how):
+        index = self.create_index()
+        if index.is_unique:
+            joined = index.join(index, how=how)
+            assert (index == joined).all()
diff --git a/pandas/tests/indexes/period/test_period.py b/pandas/tests/indexes/period/test_period.py
index 6f73e7c15e4d9..291ca317f8fae 100644
--- a/pandas/tests/indexes/period/test_period.py
+++ b/pandas/tests/indexes/period/test_period.py
@@ -773,3 +773,9 @@ def test_map(self):
         result = index.map(lambda x: x.ordinal)
         exp = Index([x.ordinal for x in index])
         tm.assert_index_equal(result, exp)
+
+    @pytest.mark.parametrize('how', ['outer', 'inner', 'left', 'right'])
+    def test_join_self(self, how):
+        index = period_range('1/1/2000', periods=10)
+        joined = index.join(index, how=how)
+        assert index is joined