diff --git a/pyproject.toml b/pyproject.toml
index f27ebcfa5..8ca874e63 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -30,7 +30,7 @@ classifiers = [
 ]
 license = {text="BSD"}
 dependencies = [
-  "msgpack >=1.0.3, <=1.0.5",
+  "msgpack >=1.0.3, <=1.0.6rc1",
   "packaging",
   "platformdirs >=3.0.0, <4.0.0; sys_platform == 'darwin'",  # for macOS: breaking changes in 3.0.0,
   "platformdirs >=2.6.0, <4.0.0; sys_platform != 'darwin'",  # for others: 2.6+ works consistently.
diff --git a/src/borg/helpers/msgpack.py b/src/borg/helpers/msgpack.py
index 54c3b9cbd..2cd708e17 100644
--- a/src/borg/helpers/msgpack.py
+++ b/src/borg/helpers/msgpack.py
@@ -209,7 +209,7 @@ def is_supported_msgpack():
 
     if msgpack.version in []:  # < add bad releases here to deny list
         return False
-    return (1, 0, 3) <= msgpack.version <= (1, 0, 5)
+    return (1, 0, 3) <= msgpack.version < (1, 0, 7)
 
 
 def get_limited_unpacker(kind):