diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 1890d7b31bed2..5150532c8ce7f 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -539,6 +539,7 @@ Datetimelike
 - Bug in adding :class:`DateOffset` with nonzero month to :class:`DatetimeIndex` would raise ``ValueError`` (:issue:`26258`)
 - Bug in :func:`to_datetime` which raises unhandled ``OverflowError`` when called with mix of invalid dates and ``NaN`` values with ``format='%Y%m%d'`` and ``error='coerce'`` (:issue:`25512`)
 - Bug in :func:`to_datetime` which raises ``TypeError`` for ``format='%Y%m%d'`` when called for invalid integer dates with length >= 6 digits with ``errors='ignore'``
+- Bug when comparing a :class:`PeriodIndex` against a zero-dimensional numpy array (:issue:`26689`)
 
 Timedelta
 ^^^^^^^^^
@@ -546,6 +547,7 @@ Timedelta
 - Bug in :func:`TimedeltaIndex.intersection` where for non-monotonic indices in some cases an empty ``Index`` was returned when in fact an intersection existed (:issue:`25913`)
 - Bug with comparisons between :class:`Timedelta` and ``NaT`` raising ``TypeError`` (:issue:`26039`)
 - Bug when adding or subtracting a :class:`BusinessHour` to a :class:`Timestamp` with the resulting time landing in a following or prior day respectively (:issue:`26381`)
+- Bug when comparing a :class:`TimedeltaIndex` against a zero-dimensional numpy array (:issue:`26689`)
 
 Timezones
 ^^^^^^^^^
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index 8a6640e11ad74..a6e282462af68 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -4,6 +4,7 @@
 
 import numpy as np
 
+from pandas._libs import lib
 from pandas._libs.tslibs import (
     NaT, NaTType, frequencies as libfrequencies, iNaT, period as libperiod)
 from pandas._libs.tslibs.fields import isleapyear_arr
@@ -51,6 +52,7 @@ def _period_array_cmp(cls, op):
     def wrapper(self, other):
         op = getattr(self.asi8, opname)
 
+        other = lib.item_from_zerodim(other)
         if isinstance(other, (ABCDataFrame, ABCSeries, ABCIndexClass)):
             return NotImplemented
 
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index 58d9e4085a612..3ba6829b4ac28 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -62,6 +62,7 @@ def _td_array_cmp(cls, op):
     nat_result = opname == '__ne__'
 
     def wrapper(self, other):
+        other = lib.item_from_zerodim(other)
         if isinstance(other, (ABCDataFrame, ABCSeries, ABCIndexClass)):
             return NotImplemented
 
diff --git a/pandas/tests/arithmetic/test_datetime64.py b/pandas/tests/arithmetic/test_datetime64.py
index 13adae279c989..afd29852fea7e 100644
--- a/pandas/tests/arithmetic/test_datetime64.py
+++ b/pandas/tests/arithmetic/test_datetime64.py
@@ -37,6 +37,7 @@ def assert_all(obj):
 # ------------------------------------------------------------------
 # Comparisons
 
+
 class TestDatetime64DataFrameComparison:
     @pytest.mark.parametrize('timestamps', [
         [pd.Timestamp('2012-01-01 13:00:00+00:00')] * 2,
@@ -338,6 +339,17 @@ def test_comparison_tzawareness_compat(self, op):
 
 class TestDatetimeIndexComparisons:
 
+    # TODO: parametrize over box
+    def test_compare_zerodim(self, tz_naive_fixture):
+        # Test comparison with zero-dimensional array is unboxed
+        tz = tz_naive_fixture
+        dti = date_range('20130101', periods=3, tz=tz)
+
+        other = np.array(dti.to_numpy()[0])
+        result = dti <= other
+        expected = np.array([True, False, False])
+        tm.assert_numpy_array_equal(result, expected)
+
     # TODO: moved from tests.indexes.test_base; parametrize and de-duplicate
     @pytest.mark.parametrize("op", [
         operator.eq, operator.ne, operator.gt, operator.lt,
diff --git a/pandas/tests/arithmetic/test_period.py b/pandas/tests/arithmetic/test_period.py
index 935f6817dcb4c..e254312e39724 100644
--- a/pandas/tests/arithmetic/test_period.py
+++ b/pandas/tests/arithmetic/test_period.py
@@ -22,6 +22,16 @@
 
 class TestPeriodIndexComparisons:
 
+    # TODO: parameterize over boxes
+    def test_compare_zerodim(self):
+        # GH#26689 make sure we unbox zero-dimensional arrays
+        pi = pd.period_range('2000', periods=4)
+        other = np.array(pi.to_numpy()[0])
+
+        result = pi <= other
+        expected = np.array([True, False, False, False])
+        tm.assert_numpy_array_equal(result, expected)
+
     @pytest.mark.parametrize("other", ["2017", 2017])
     def test_eq(self, other):
         idx = PeriodIndex(['2017', '2017', '2018'], freq="D")
diff --git a/pandas/tests/arithmetic/test_timedelta64.py b/pandas/tests/arithmetic/test_timedelta64.py
index c214a880345ae..56f47324967a1 100644
--- a/pandas/tests/arithmetic/test_timedelta64.py
+++ b/pandas/tests/arithmetic/test_timedelta64.py
@@ -33,6 +33,19 @@ def get_upcast_box(box, vector):
 class TestTimedelta64ArrayComparisons:
     # TODO: All of these need to be parametrized over box
 
+    def test_compare_timedelta64_zerodim(self):
+        # GH#26689 should unbox when comparing with zerodim array
+        tdi = pd.timedelta_range('2H', periods=4)
+        other = np.array(tdi.to_numpy()[0])
+
+        res = tdi <= other
+        expected = np.array([True, False, False, False])
+        tm.assert_numpy_array_equal(res, expected)
+
+        with pytest.raises(TypeError):
+            # zero-dim of wrong dtype should still raise
+            tdi >= np.array(4)
+
     def test_compare_timedelta_series(self):
         # regresssion test for GH#5963
         s = pd.Series([timedelta(days=1), timedelta(days=2)])