diff --git a/ipykernel/ipkernel.py b/ipykernel/ipkernel.py
index db83d986..9d201e32 100644
--- a/ipykernel/ipkernel.py
+++ b/ipykernel/ipkernel.py
@@ -411,6 +411,7 @@ async def run(execution: Execution) -> None:
                 try:
                     async with create_task_group() as tg:
                         execution = Execution()
+                        self.shell_is_blocking = False
                         self.shell_is_awaiting = True
                         tg.start_soon(run, execution)
                         execution.interrupt = await to_thread.run_sync(self.shell_interrupt.get)
diff --git a/ipykernel/kernelbase.py b/ipykernel/kernelbase.py
index 64a93527..bb8535b0 100644
--- a/ipykernel/kernelbase.py
+++ b/ipykernel/kernelbase.py
@@ -659,7 +659,9 @@ async def execute_request(self, socket, ident, parent):
             do_execute_args["cell_id"] = cell_id
 
         # Call do_execute with the appropriate arguments
+        self.shell_is_blocking = True
         reply_content = self.do_execute(**do_execute_args)
+        self.shell_is_blocking = False
 
         if inspect.isawaitable(reply_content):
             reply_content = await reply_content