diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 7b17a519d169e..7ea6fc253c60b 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5422,7 +5422,7 @@ def _concat(self, to_concat: list[Index], name: Hashable) -> Index:
 
         result = concat_compat(to_concat_vals)
 
-        return Index._with_infer(result, name=name)
+        return Index._with_infer(result, name=name, copy=False)
 
     def putmask(self, mask, value) -> Index:
         """
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index bf05dbd40145f..4a935c2afb43e 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -1246,7 +1246,7 @@ def _concat(self, indexes: list[Index], name: Hashable) -> Index:
                     )
                 else:
                     values = np.concatenate([x._values for x in rng_indexes])
-                result = self._constructor(values)
+                result = self._constructor(values, copy=False)
                 return result.rename(name)
 
             if step is not None: