diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index a6c92bf9faf9b..239c9b9fbe1c9 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -1065,6 +1065,7 @@ Indexing
 - Bug in ``Index`` subclasses constructors that ignore unexpected keyword arguments (:issue:`19348`)
 - Bug in :meth:`Index.difference` when taking difference of an ``Index`` with itself (:issue:`20040`)
 - Bug in :meth:`DataFrame.first_valid_index` and :meth:`DataFrame.last_valid_index` in presence of entire rows of NaNs in the middle of values (:issue:`20499`).
+- Bug in :class:`IntervalIndex` where some indexing operations were not supported for overlapping or non-monotonic ``uint64`` data (:issue:`20636`)
 
 MultiIndex
 ^^^^^^^^^^
diff --git a/pandas/_libs/intervaltree.pxi.in b/pandas/_libs/intervaltree.pxi.in
index b22e694c9fcca..9ed76242a95c3 100644
--- a/pandas/_libs/intervaltree.pxi.in
+++ b/pandas/_libs/intervaltree.pxi.in
@@ -5,7 +5,7 @@ WARNING: DO NOT edit .pxi FILE directly, .pxi is generated from .pxi.in
 """
 
 from numpy cimport (
-    int64_t, int32_t, float64_t, float32_t,
+    int64_t, int32_t, float64_t, float32_t, uint64_t,
     ndarray,
     PyArray_ArgSort, NPY_QUICKSORT, PyArray_Take)
 import numpy as np
@@ -24,6 +24,7 @@ ctypedef fused scalar_t:
     float32_t
     int64_t
     int32_t
+    uint64_t
 
 
 #----------------------------------------------------------------------
@@ -205,7 +206,7 @@ cdef sort_values_and_indices(all_values, all_indices, subset):
 {{py:
 
 nodes = []
-for dtype in ['float32', 'float64', 'int32', 'int64']:
+for dtype in ['float32', 'float64', 'int32', 'int64', 'uint64']:
     for closed, cmp_left, cmp_right in [
         ('left', '<=', '<'),
         ('right', '<', '<='),
diff --git a/pandas/tests/indexes/interval/test_interval_tree.py b/pandas/tests/indexes/interval/test_interval_tree.py
index 343131125f640..056d3e1087a2e 100644
--- a/pandas/tests/indexes/interval/test_interval_tree.py
+++ b/pandas/tests/indexes/interval/test_interval_tree.py
@@ -12,36 +12,37 @@ def closed(request):
     return request.param
 
 
+@pytest.fixture(
+    scope='class', params=['int32', 'int64', 'float32', 'float64', 'uint64'])
+def dtype(request):
+    return request.param
+
+
+@pytest.fixture(scope='class')
+def tree(dtype):
+    left = np.arange(5, dtype=dtype)
+    return IntervalTree(left, left + 2)
+
+
 class TestIntervalTree(object):
-    def setup_method(self, method):
-        def gentree(dtype):
-            left = np.arange(5, dtype=dtype)
-            right = left + 2
-            return IntervalTree(left, right)
-
-        self.tree = gentree('int64')
-        self.trees = {dtype: gentree(dtype)
-                      for dtype in ['int32', 'int64', 'float32', 'float64']}
-
-    def test_get_loc(self):
-        for dtype, tree in self.trees.items():
-            tm.assert_numpy_array_equal(tree.get_loc(1),
-                                        np.array([0], dtype='int64'))
-            tm.assert_numpy_array_equal(np.sort(tree.get_loc(2)),
-                                        np.array([0, 1], dtype='int64'))
-            with pytest.raises(KeyError):
-                tree.get_loc(-1)
-
-    def test_get_indexer(self):
-        for dtype, tree in self.trees.items():
-            tm.assert_numpy_array_equal(
-                tree.get_indexer(np.array([1.0, 5.5, 6.5])),
-                np.array([0, 4, -1], dtype='int64'))
-            with pytest.raises(KeyError):
-                tree.get_indexer(np.array([3.0]))
-
-    def test_get_indexer_non_unique(self):
-        indexer, missing = self.tree.get_indexer_non_unique(
+
+    def test_get_loc(self, tree):
+        tm.assert_numpy_array_equal(tree.get_loc(1),
+                                    np.array([0], dtype='int64'))
+        tm.assert_numpy_array_equal(np.sort(tree.get_loc(2)),
+                                    np.array([0, 1], dtype='int64'))
+        with pytest.raises(KeyError):
+            tree.get_loc(-1)
+
+    def test_get_indexer(self, tree):
+        tm.assert_numpy_array_equal(
+            tree.get_indexer(np.array([1.0, 5.5, 6.5])),
+            np.array([0, 4, -1], dtype='int64'))
+        with pytest.raises(KeyError):
+            tree.get_indexer(np.array([3.0]))
+
+    def test_get_indexer_non_unique(self, tree):
+        indexer, missing = tree.get_indexer_non_unique(
             np.array([1.0, 2.0, 6.5]))
         tm.assert_numpy_array_equal(indexer[:1],
                                     np.array([0], dtype='int64'))
@@ -51,8 +52,9 @@ def test_get_indexer_non_unique(self):
                                     np.array([-1], dtype='int64'))
         tm.assert_numpy_array_equal(missing, np.array([2], dtype='int64'))
 
-    def test_duplicates(self):
-        tree = IntervalTree([0, 0, 0], [1, 1, 1])
+    def test_duplicates(self, dtype):
+        left = np.array([0, 0, 0], dtype=dtype)
+        tree = IntervalTree(left, left + 1)
         tm.assert_numpy_array_equal(np.sort(tree.get_loc(0.5)),
                                     np.array([0, 1, 2], dtype='int64'))