diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 61848cb127029..4ad3f9e2ea391 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -786,6 +786,8 @@ Indexing
 - Bug in :meth:`Series.asof` and :meth:`DataFrame.asof` incorrectly casting bool-dtype results to ``float64`` dtype (:issue:`16063`)
 - Bug in :meth:`NDFrame.xs`, :meth:`DataFrame.iterrows`, :meth:`DataFrame.loc` and :meth:`DataFrame.iloc` not always propagating metadata (:issue:`28283`)
 - Bug in :meth:`DataFrame.sum` min_count changes dtype if input contains NaNs (:issue:`46947`)
+- Bug in :class:`IntervalTree` that lead to an infinite recursion. (:issue:`46658`)
+-
 
 Missing
 ^^^^^^^
diff --git a/pandas/_libs/intervaltree.pxi.in b/pandas/_libs/intervaltree.pxi.in
index 51db5f1e76c99..9842332bae7ef 100644
--- a/pandas/_libs/intervaltree.pxi.in
+++ b/pandas/_libs/intervaltree.pxi.in
@@ -342,6 +342,13 @@ cdef class {{dtype_title}}Closed{{closed_title}}IntervalNode(IntervalNode):
             # calculate a pivot so we can create child nodes
             self.is_leaf_node = False
             self.pivot = np.median(left / 2 + right / 2)
+            if np.isinf(self.pivot):
+                self.pivot = cython.cast({{dtype}}_t, 0)
+                if self.pivot > np.max(right):
+                    self.pivot = np.max(left)
+                if self.pivot < np.min(left):
+                    self.pivot = np.min(right)
+
             left_set, right_set, center_set = self.classify_intervals(
                 left, right)
 
diff --git a/pandas/tests/indexes/interval/test_interval_tree.py b/pandas/tests/indexes/interval/test_interval_tree.py
index 345025d63f4b2..06c499b9e33f4 100644
--- a/pandas/tests/indexes/interval/test_interval_tree.py
+++ b/pandas/tests/indexes/interval/test_interval_tree.py
@@ -207,3 +207,21 @@ def test_interval_tree_error_and_warning(self):
         ):
             left, right = np.arange(10), [np.iinfo(np.int64).max] * 10
             IntervalTree(left, right, closed="both")
+
+    @pytest.mark.xfail(not IS64, reason="GH 23440")
+    @pytest.mark.parametrize(
+        "left, right, expected",
+        [
+            ([-np.inf, 1.0], [1.0, 2.0], 0.0),
+            ([-np.inf, -2.0], [-2.0, -1.0], -2.0),
+            ([-2.0, -1.0], [-1.0, np.inf], 0.0),
+            ([1.0, 2.0], [2.0, np.inf], 2.0),
+        ],
+    )
+    def test_inf_bound_infinite_recursion(self, left, right, expected):
+        # GH 46658
+
+        tree = IntervalTree(left * 101, right * 101)
+
+        result = tree.root.pivot
+        assert result == expected
diff --git a/pandas/tests/indexing/interval/test_interval_new.py b/pandas/tests/indexing/interval/test_interval_new.py
index 2e3c765b2b372..602f45d637afb 100644
--- a/pandas/tests/indexing/interval/test_interval_new.py
+++ b/pandas/tests/indexing/interval/test_interval_new.py
@@ -3,7 +3,10 @@
 import numpy as np
 import pytest
 
+from pandas.compat import IS64
+
 from pandas import (
+    Index,
     Interval,
     IntervalIndex,
     Series,
@@ -217,3 +220,24 @@ def test_loc_getitem_missing_key_error_message(
         obj = frame_or_series(ser)
         with pytest.raises(KeyError, match=r"\[6\]"):
             obj.loc[[4, 5, 6]]
+
+
+@pytest.mark.xfail(not IS64, reason="GH 23440")
+@pytest.mark.parametrize(
+    "intervals",
+    [
+        ([Interval(-np.inf, 0.0), Interval(0.0, 1.0)]),
+        ([Interval(-np.inf, -2.0), Interval(-2.0, -1.0)]),
+        ([Interval(-1.0, 0.0), Interval(0.0, np.inf)]),
+        ([Interval(1.0, 2.0), Interval(2.0, np.inf)]),
+    ],
+)
+def test_repeating_interval_index_with_infs(intervals):
+    # GH 46658
+
+    interval_index = Index(intervals * 51)
+
+    expected = np.arange(1, 102, 2, dtype=np.intp)
+    result = interval_index.get_indexer_for([intervals[1]])
+
+    tm.assert_equal(result, expected)