diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 94eb9a0b3fc58..cb4d04d4443e7 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -831,6 +831,7 @@ Other
 - Bug in :meth:`Index.difference` failing to set the correct name on the returned :class:`Index` in some corner cases (:issue:`38268`)
 - Bug in :meth:`Index.union` behaving differently depending on whether operand is an :class:`Index` or other list-like (:issue:`36384`)
 - Bug in :meth:`Index.intersection` with non-matching numeric dtypes casting to ``object`` dtype instead of minimal common dtype (:issue:`38122`)
+- Bug in :meth:`IntervalIndex.intersection` returning an incorrectly-typed :class:`Index` when empty (:issue:`38282`)
 - Passing an array with 2 or more dimensions to the :class:`Series` constructor now raises the more specific ``ValueError`` rather than a bare ``Exception`` (:issue:`35744`)
 - Bug in ``dir`` where ``dir(obj)`` wouldn't show attributes defined on the instance for pandas objects (:issue:`37173`)
 - Bug in :meth:`Index.drop` raising ``InvalidIndexError`` when index has duplicates (:issue:`38051`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index c0840d8e0d4b0..ba958b23e81af 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -2694,7 +2694,7 @@ def union(self, other, sort=None):
         """
         self._validate_sort_keyword(sort)
         self._assert_can_do_setop(other)
-        other = ensure_index(other)
+        other, result_name = self._convert_can_do_setop(other)
 
         if not self._can_union_without_object_cast(other):
             return self._union_incompatible_dtypes(other, sort=sort)
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 3036e944d1e51..2f86d9c20bfe8 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -1060,6 +1060,10 @@ def _intersection_non_unique(self, other: "IntervalIndex") -> "IntervalIndex":
 
     def _setop(op_name: str, sort=None):
         def func(self, other, sort=sort):
+            # At this point we are assured
+            #  isinstance(other, IntervalIndex)
+            #  other.closed == self.closed
+
             result = getattr(self._multiindex, op_name)(other._multiindex, sort=sort)
             result_name = get_op_result_name(self, other)
 
@@ -1074,7 +1078,7 @@ def func(self, other, sort=sort):
         func.__name__ = op_name
         return setop_check(func)
 
-    union = _setop("union")
+    _union = _setop("union")
     difference = _setop("difference")
     symmetric_difference = _setop("symmetric_difference")
 
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 911bbc44bb599..fd47c23b7c92b 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -3569,6 +3569,11 @@ def union(self, other, sort=None):
         if len(other) == 0 or self.equals(other):
             return self.rename(result_names)
 
+        return self._union(other, sort=sort)
+
+    def _union(self, other, sort):
+        other, result_names = self._convert_can_do_setop(other)
+
         # TODO: Index.union returns other when `len(self)` is 0.
 
         if not is_object_dtype(other.dtype):
diff --git a/pandas/tests/indexes/interval/test_setops.py b/pandas/tests/indexes/interval/test_setops.py
index 0b94d70367b4d..0ef833bb93ded 100644
--- a/pandas/tests/indexes/interval/test_setops.py
+++ b/pandas/tests/indexes/interval/test_setops.py
@@ -32,15 +32,17 @@ def test_union(self, closed, sort):
         tm.assert_index_equal(index.union(index, sort=sort), index)
         tm.assert_index_equal(index.union(index[:1], sort=sort), index)
 
+    def test_union_empty_result(self, closed, sort):
         # GH 19101: empty result, same dtype
         index = empty_index(dtype="int64", closed=closed)
         result = index.union(index, sort=sort)
         tm.assert_index_equal(result, index)
 
-        # GH 19101: empty result, different dtypes
+        # GH 19101: empty result, different dtypes -> common dtype is object
         other = empty_index(dtype="float64", closed=closed)
         result = index.union(other, sort=sort)
-        tm.assert_index_equal(result, index)
+        expected = Index([], dtype=object)
+        tm.assert_index_equal(result, expected)
 
     def test_intersection(self, closed, sort):
         index = monotonic_index(0, 11, closed=closed)