diff --git a/ipykernel/kernelapp.py b/ipykernel/kernelapp.py
index 41ffbcc39..667df15d9 100644
--- a/ipykernel/kernelapp.py
+++ b/ipykernel/kernelapp.py
@@ -460,6 +460,10 @@ def close(self):
             self.log.debug("Closing iopub channel")
             self.iopub_thread.stop()
             self.iopub_thread.close()
+        elif self.iopub_socket is not None and not self.iopub_socket.closed:
+            # The iopub port could not be bound, so no IOPub thread owns the socket.
+            # Left open, it would block context.term() below.
+            self.iopub_socket.close()
         if self.control_thread and self.control_thread.is_alive():
             self.log.debug("Closing control thread")
             self.control_thread.stop()
diff --git a/tests/test_kernelapp.py b/tests/test_kernelapp.py
index 44a06886a..21fbc3ad9 100644
--- a/tests/test_kernelapp.py
+++ b/tests/test_kernelapp.py
@@ -1,10 +1,13 @@
+import atexit
 import json
 import os
+import socket
 import threading
 import time
 from unittest.mock import patch
 
 import pytest
+import zmq
 from jupyter_client import KernelManager
 from jupyter_client.kernelspec import KernelSpecManager
 from jupyter_core.paths import secure_write
@@ -30,6 +33,21 @@ def test_init_ipc_socket():
     app.close()
 
 
+def test_close_after_iopub_port_in_use():
+    app = IPKernelApp(transport="tcp")
+    with socket.socket() as taken:
+        taken.bind((app.ip, 0))
+        taken.listen(1)
+        app.iopub_port = taken.getsockname()[1]
+        with pytest.raises(zmq.ZMQError):
+            app.init_sockets()
+    atexit.unregister(app.close)
+    closing = threading.Thread(target=app.close, daemon=True)
+    closing.start()
+    closing.join(timeout=10)
+    assert not closing.is_alive(), "close() is still waiting for the zmq context to terminate"
+
+
 def test_blackhole():
     app = IPKernelApp()
     app.no_stderr = True