diff --git a/jax/_src/api.py b/jax/_src/api.py
index cbc75b305208..44852e335fc2 100644
--- a/jax/_src/api.py
+++ b/jax/_src/api.py
@@ -28,11 +28,13 @@
 from functools import partial
 import inspect
 import math
-from typing import Any, Callable, Literal, NamedTuple, TypeVar, cast, overload
+from typing import (Any, Callable, Literal, NamedTuple, TypeVar, cast,
+                    overload, TYPE_CHECKING)
 import weakref
 
 import numpy as np
-from typing_extensions import ParamSpec
+if TYPE_CHECKING:
+  from typing_extensions import ParamSpec
 
 from jax._src import linear_util as lu
 from jax._src import stages
@@ -94,7 +96,8 @@
 T = TypeVar("T")
 U = TypeVar("U")
 V_co = TypeVar("V_co", covariant=True)
-P = ParamSpec("P")
+if TYPE_CHECKING:
+  P = ParamSpec("P")
 
 
 map, unsafe_map = safe_map, map
diff --git a/jax/_src/stages.py b/jax/_src/stages.py
index 0e050817b0e7..2bb677ec40f1 100644
--- a/jax/_src/stages.py
+++ b/jax/_src/stages.py
@@ -32,8 +32,10 @@
 
 from collections.abc import Sequence
 from dataclasses import dataclass
-from typing import Any, Generic, NamedTuple, Protocol, TypeVar, Union
-from typing_extensions import ParamSpec
+from typing import (Any, Generic, NamedTuple, Protocol, TypeVar, Union,
+                    TYPE_CHECKING)
+if TYPE_CHECKING:
+  from typing_extensions import ParamSpec
 
 import jax
 
@@ -648,7 +650,10 @@ def cost_analysis(self) -> Any | None:
 
 
 V_co = TypeVar("V_co", covariant=True)
-P = ParamSpec("P")
+if TYPE_CHECKING:
+  P = ParamSpec("P")
+else:
+  P = TypeVar("P")
 
 
 class Wrapped(Protocol, Generic[P, V_co]):
diff --git a/setup.py b/setup.py
index bec977b14d0a..857c42f23cff 100644
--- a/setup.py
+++ b/setup.py
@@ -84,9 +84,9 @@ def generate_proto(source):
         # Python versions < 3.10. Can be dropped when 3.10 is the minimum
         # required Python version.
         'importlib_metadata>=4.6;python_version<"3.10"',
-        'typing_extensions>=4.5.0',
     ],
     extras_require={
+        'dev': ['typing_extensions>=4.8.0'],
         # Minimum jaxlib version; used in testing.
         'minimum-jaxlib': [f'jaxlib=={_minimum_jaxlib_version}'],