diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index e6f59f8518754..f9e382285b408 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -321,6 +321,9 @@ cdef class IndexEngine:
             if is_strict_monotonic:
                 self.unique = 1
                 self.need_unique_check = 0
+            elif self.monotonic_inc == 1 or self.monotonic_dec == 1:
+                self.unique = 0
+                self.need_unique_check = 0
 
     cdef _call_monotonic(self, values):
         return algos.is_monotonic(values, timelike=False)