diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index fe8d028150403d..3618bcb6d7c6b5 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -426,6 +426,9 @@ Sleeping
    .. versionchanged:: 3.10
       Removed the *loop* parameter.
 
+   .. versionchanged:: 3.13
+      Raises :exc:`ValueError` if *delay* is :data:`~math.nan`.
+
 
 Running Tasks Concurrently
 ==========================
diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 8d5bde09ea9b5b..4250bb0753879a 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -15,6 +15,7 @@
 import functools
 import inspect
 import itertools
+import math
 import types
 import warnings
 import weakref
@@ -646,6 +647,9 @@ async def sleep(delay, result=None):
         await __sleep0()
         return result
 
+    if math.isnan(delay):
+        raise ValueError("Invalid delay: NaN (not a number)")
+
     loop = events.get_running_loop()
     future = loop.create_future()
     h = loop.call_later(delay,
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 6e8a51ce2555d5..4dfaff847edb90 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -1609,6 +1609,21 @@ async def sleeper(dt, arg):
         self.assertEqual(t.result(), 'yeah')
         self.assertAlmostEqual(0.1, loop.time())
 
+    def test_sleep_when_delay_is_nan(self):
+
+        def gen():
+            yield
+
+        loop = self.new_test_loop(gen)
+
+        async def sleeper():
+            await asyncio.sleep(float("nan"))
+
+        t = self.new_task(loop, sleeper())
+
+        with self.assertRaises(ValueError):
+            loop.run_until_complete(t)
+
     def test_sleep_cancel(self):
 
         def gen():
diff --git a/Misc/NEWS.d/next/Core and Builtins/2023-06-11-09-14-30.gh-issue-105331.nlZvoW.rst b/Misc/NEWS.d/next/Core and Builtins/2023-06-11-09-14-30.gh-issue-105331.nlZvoW.rst
new file mode 100644
index 00000000000000..4a3fee0dd64ae0
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2023-06-11-09-14-30.gh-issue-105331.nlZvoW.rst	
@@ -0,0 +1,2 @@
+Raise :exc:`ValueError` if the ``delay`` argument to :func:`asyncio.sleep` is a NaN (matching :func:`time.sleep`).
+