diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 95387c9557b1a..e8b68d41983d5 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3059,6 +3059,7 @@ def _union(self, other: Index, sort):
             and self.is_monotonic
             and other.is_monotonic
             and not (self.has_duplicates and other.has_duplicates)
+            and self._can_use_libjoin
         ):
             # Both are unique and monotonic, so can use outer join
             try:
@@ -3189,13 +3190,7 @@ def _intersection(self, other: Index, sort=False):
         """
         intersection specialized to the case with matching dtypes.
         """
-        if (
-            self.is_monotonic
-            and other.is_monotonic
-            and not is_interval_dtype(self.dtype)
-        ):
-            # For IntervalIndex _inner_indexer is not more performant than get_indexer,
-            #  so don't take this fastpath
+        if self.is_monotonic and other.is_monotonic and self._can_use_libjoin:
             try:
                 result = self._inner_indexer(other)[0]
             except TypeError:
@@ -4178,12 +4173,15 @@ def join(
             return self._join_non_unique(other, how=how)
         elif not self.is_unique or not other.is_unique:
             if self.is_monotonic and other.is_monotonic:
-                return self._join_monotonic(other, how=how)
+                if self._can_use_libjoin:
+                    # otherwise we will fall through to _join_via_get_indexer
+                    return self._join_monotonic(other, how=how)
             else:
                 return self._join_non_unique(other, how=how)
         elif (
             self.is_monotonic
             and other.is_monotonic
+            and self._can_use_libjoin
             and (
                 not isinstance(self, ABCMultiIndex)
                 or not any(is_categorical_dtype(dtype) for dtype in self.dtypes)
@@ -4545,6 +4543,15 @@ def _wrap_joined_index(self: _IndexT, joined: ArrayLike, other: _IndexT) -> _Ind
             name = get_op_result_name(self, other)
             return self._constructor._with_infer(joined, name=name)
 
+    @cache_readonly
+    def _can_use_libjoin(self) -> bool:
+        """
+        Whether we can use the fastpaths implement in _libs.join
+        """
+        # Note: this will need to be updated when e.g. Nullable dtypes
+        #  are supported in Indexes.
+        return not is_interval_dtype(self.dtype)
+
     # --------------------------------------------------------------------
     # Uncategorized Methods
 
diff --git a/pandas/core/indexes/extension.py b/pandas/core/indexes/extension.py
index 44267895a989e..a7930ac83a96a 100644
--- a/pandas/core/indexes/extension.py
+++ b/pandas/core/indexes/extension.py
@@ -246,11 +246,6 @@ def searchsorted(
     def _get_engine_target(self) -> np.ndarray:
         return np.asarray(self._data)
 
-    def _from_join_target(self, result: np.ndarray) -> ArrayLike:
-        # ATM this is only for IntervalIndex, implicit assumption
-        #  about _get_engine_target
-        return type(self._data)._from_sequence(result, dtype=self.dtype)
-
     def delete(self, loc):
         """
         Make new Index with passed location(-s) deleted
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 0b9b818b960a0..c74a1b1ea60fd 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -38,7 +38,6 @@
 from pandas.util._exceptions import rewrite_exception
 
 from pandas.core.dtypes.cast import (
-    construct_1d_object_array_from_listlike,
     find_common_type,
     infer_dtype_from_scalar,
     maybe_box_datetimelike,
@@ -894,17 +893,13 @@ def _is_all_dates(self) -> bool:
         return False
 
     def _get_join_target(self) -> np.ndarray:
-        # constructing tuples is much faster than constructing Intervals
-        tups = list(zip(self.left, self.right))
-        target = construct_1d_object_array_from_listlike(tups)
-        return target
+        # Note: we _could_ use libjoin functions by either casting to object
+        #  dtype or constructing tuples (faster than constructing Intervals)
+        #  but the libjoin fastpaths are no longer fast in these cases.
+        raise NotImplementedError("IntervalIndex does not use libjoin fastpaths")
 
     def _from_join_target(self, result):
-        left, right = list(zip(*result))
-        arr = type(self._data).from_arrays(
-            left, right, dtype=self.dtype, closed=self.closed
-        )
-        return type(self)._simple_new(arr, name=self.name)
+        raise NotImplementedError("IntervalIndex does not use libjoin fastpaths")
 
     # TODO: arithmetic operations