diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index e3c4e69db7cbd..846d863910b4c 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -547,6 +547,7 @@ Strings
 
 Interval
 ^^^^^^^^
+- :meth:`Index.is_monotonic_decreasing`, :meth:`Index.is_monotonic_increasing`, and :meth:`Index.is_unique` could incorrectly be ``False`` for an ``Index`` created from a slice of another ``Index``. (:issue:`57911`)
 - Bug in :func:`interval_range` where start and end numeric types were always cast to 64 bit (:issue:`57268`)
 -
 
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index f1be8d97c71eb..1506a76aa94a6 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -252,14 +252,24 @@ cdef class IndexEngine:
         return self.sizeof()
 
     cpdef _update_from_sliced(self, IndexEngine other, reverse: bool):
-        self.unique = other.unique
-        self.need_unique_check = other.need_unique_check
+        if other.unique:
+            self.unique = other.unique
+            self.need_unique_check = other.need_unique_check
+
         if not other.need_monotonic_check and (
                 other.is_monotonic_increasing or other.is_monotonic_decreasing):
-            self.need_monotonic_check = other.need_monotonic_check
-            # reverse=True means the index has been reversed
-            self.monotonic_inc = other.monotonic_dec if reverse else other.monotonic_inc
-            self.monotonic_dec = other.monotonic_inc if reverse else other.monotonic_dec
+            self.need_monotonic_check = 0
+            if len(self.values) > 0 and self.values[0] != self.values[-1]:
+                # reverse=True means the index has been reversed
+                if reverse:
+                    self.monotonic_inc = other.monotonic_dec
+                    self.monotonic_dec = other.monotonic_inc
+                else:
+                    self.monotonic_inc = other.monotonic_inc
+                    self.monotonic_dec = other.monotonic_dec
+            else:
+                self.monotonic_inc = 1
+                self.monotonic_dec = 1
 
     @property
     def is_unique(self) -> bool:
@@ -882,14 +892,24 @@ cdef class SharedEngine:
         pass
 
     cpdef _update_from_sliced(self, ExtensionEngine other, reverse: bool):
-        self.unique = other.unique
-        self.need_unique_check = other.need_unique_check
+        if other.unique:
+            self.unique = other.unique
+            self.need_unique_check = other.need_unique_check
+
         if not other.need_monotonic_check and (
                 other.is_monotonic_increasing or other.is_monotonic_decreasing):
-            self.need_monotonic_check = other.need_monotonic_check
-            # reverse=True means the index has been reversed
-            self.monotonic_inc = other.monotonic_dec if reverse else other.monotonic_inc
-            self.monotonic_dec = other.monotonic_inc if reverse else other.monotonic_dec
+            self.need_monotonic_check = 0
+            if len(self.values) > 0 and self.values[0] != self.values[-1]:
+                # reverse=True means the index has been reversed
+                if reverse:
+                    self.monotonic_inc = other.monotonic_dec
+                    self.monotonic_dec = other.monotonic_inc
+                else:
+                    self.monotonic_inc = other.monotonic_inc
+                    self.monotonic_dec = other.monotonic_dec
+            else:
+                self.monotonic_inc = 1
+                self.monotonic_dec = 1
 
     @property
     def is_unique(self) -> bool:
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index 16908fbb4fecc..8d2245d0d9978 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -961,6 +961,31 @@ def test_slice_keep_name(self):
         index = Index(["a", "b"], name="asdf")
         assert index.name == index[1:].name
 
+    def test_slice_is_unique(self):
+        # GH 57911
+        index = Index([1, 1, 2, 3, 4])
+        assert not index.is_unique
+        filtered_index = index[2:].copy()
+        assert filtered_index.is_unique
+
+    def test_slice_is_montonic(self):
+        """Test that is_monotonic_decreasing is correct on slices."""
+        # GH 57911
+        index = Index([1, 2, 3, 3])
+        assert not index.is_monotonic_decreasing
+
+        filtered_index = index[2:].copy()
+        assert filtered_index.is_monotonic_decreasing
+        assert filtered_index.is_monotonic_increasing
+
+        filtered_index = index[1:].copy()
+        assert not filtered_index.is_monotonic_decreasing
+        assert filtered_index.is_monotonic_increasing
+
+        filtered_index = index[:].copy()
+        assert not filtered_index.is_monotonic_decreasing
+        assert filtered_index.is_monotonic_increasing
+
     @pytest.mark.parametrize(
         "index",
         [