diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 694f2201d9f34..725b793cc9b7a 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3900,9 +3900,10 @@ def _check_indexing_method(
                         "tolerance not implemented yet for MultiIndex"
                     )
 
-        if isinstance(self.dtype, (IntervalDtype, CategoricalDtype)):
+        if isinstance(self.dtype, (CategoricalDtype)):
             # GH#37871 for now this is only for IntervalIndex and CategoricalIndex
-            if method is not None:
+            if method is not None:  # and method not in ("bfill", "backfill")
+                # and not is_interval_dtype(self.dtype):
                 raise NotImplementedError(
                     f"method {method} not yet implemented for {type(self).__name__}"
                 )
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 13c87a9d06b66..bba0af0545576 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -702,6 +702,12 @@ def _get_indexer(
             # we should always have self._should_partial_index(target) here
             target = self._maybe_convert_i8(target)
             indexer = self._engine.get_indexer(target.values)
+
+            # if indexer is int:
+            if (indexer == [-1]).all() and method in ("bfill", "backfill"):
+                # GH#51503
+                indexer = self._get_indexer_ffill(target, method)
+
         else:
             # heterogeneous scalar index: defer elementwise to get_loc
             # we should always have self._should_partial_index(target) here
@@ -709,6 +715,25 @@ def _get_indexer(
 
         return ensure_platform_int(indexer)
 
+    def _get_indexer_ffill(self, target, method):
+        # GH#51503
+        if method in ("bfill", "backfill"):
+            temp = []
+            _len_self = len(self)
+            for i in range(_len_self):
+                # not sure to call this method for every value
+                t = self._maybe_cast_listlike_indexer([self[i]])
+                temp.append(self._maybe_convert_i8(t))
+
+            for i in range(_len_self):
+                # TODO: Comparing is not written professionally. Needs more review
+                if target[0] < temp[i].values[0].left:
+                    return [i]
+
+            return -1
+        else:
+            return -1
+
     @Appender(_index_shared_docs["get_indexer_non_unique"] % _index_doc_kwargs)
     def get_indexer_non_unique(
         self, target: Index
diff --git a/pandas/tests/indexes/interval/test_indexing.py b/pandas/tests/indexes/interval/test_indexing.py
index e7db8076efa2b..840e2ed4aed85 100644
--- a/pandas/tests/indexes/interval/test_indexing.py
+++ b/pandas/tests/indexes/interval/test_indexing.py
@@ -424,6 +424,24 @@ def test_get_indexer_interval_index(self, box):
         expected = np.array([-1, -1, -1], dtype=np.intp)
         tm.assert_numpy_array_equal(actual, expected)
 
+    def test_get_indexer_with_backfill(self):
+        # GH#51503
+        dt = Timestamp.now()
+        h = Timedelta("1h")
+
+        # 3 simple interval ranges, with a big gap between 2nd and 3rd
+        intervals = IntervalIndex.from_arrays(
+            [dt, dt + h, dt + 10 * h], [dt + h, dt + 2 * h, dt + 11 * h], closed="left"
+        )
+
+        result = intervals.get_indexer([dt + 5 * h], method="bfill")
+        # result = intervals.get_indexer([dt + 5 * h])
+        # result = intervals.get_indexer([dt + 10 * h], method="nearest")
+
+        expected = np.array([2], dtype=np.intp)
+
+        tm.assert_numpy_array_equal(result, expected)
+
 
 class TestSliceLocs:
     def test_slice_locs_with_interval(self):