diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 24fcb32d09d27..896935fa72adb 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -1140,7 +1140,10 @@ def overlaps(self, other):
 
     @Appender(_index_shared_docs['intersection'])
     @SetopCheck(op_name='intersection')
-    def intersection(self, other, sort=False):
+    def intersection(self,
+                     other: 'IntervalIndex',
+                     sort: bool = False
+                     ) -> 'IntervalIndex':
         if self.left.is_unique and self.right.is_unique:
             taken = self._intersection_unique(other)
         elif (other.left.is_unique and other.right.is_unique and
@@ -1157,7 +1160,9 @@ def intersection(self, other, sort=False):
 
         return taken
 
-    def _intersection_unique(self, other):
+    def _intersection_unique(self,
+                             other: 'IntervalIndex'
+                             ) -> 'IntervalIndex':
         """
         Used when the IntervalIndex does not have any common endpoint,
         no mater left or right.
@@ -1179,7 +1184,9 @@ def _intersection_unique(self, other):
 
         return self.take(indexer)
 
-    def _intersection_non_unique(self, other):
+    def _intersection_non_unique(self,
+                                 other: 'IntervalIndex'
+                                 ) -> 'IntervalIndex':
         """
         Used when the IntervalIndex does have some common endpoints,
         on either sides.