diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 79239ec90ac80..eb4284203d865 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -1061,6 +1061,14 @@ def func(self, other):
                                           name=result_name)
         return func
 
+    @property
+    def is_all_dates(self):
+        """
+        This is False even when left/right contain datetime-like objects,
+        as the check is done on the Interval itself
+        """
+        return False
+
     union = _setop('union')
     intersection = _setop('intersection')
     difference = _setop('difference')
diff --git a/pandas/tests/indexes/interval/test_interval.py b/pandas/tests/indexes/interval/test_interval.py
index ac0446373a6a1..258f2dc41fb79 100644
--- a/pandas/tests/indexes/interval/test_interval.py
+++ b/pandas/tests/indexes/interval/test_interval.py
@@ -1150,3 +1150,10 @@ def test_set_closed_errors(self, bad_closed):
         msg = "invalid option for 'closed': {closed}".format(closed=bad_closed)
         with tm.assert_raises_regex(ValueError, msg):
             index.set_closed(bad_closed)
+
+    def test_is_all_dates(self):
+        # GH 23576
+        year_2017 = pd.Interval(pd.Timestamp('2017-01-01 00:00:00'),
+                                pd.Timestamp('2018-01-01 00:00:00'))
+        year_2017_index = pd.IntervalIndex([year_2017])
+        assert not year_2017_index.is_all_dates