diff --git a/distributed/distributed-schema.yaml b/distributed/distributed-schema.yaml
index 45534e9be80..cf70ffdab61 100644
--- a/distributed/distributed-schema.yaml
+++ b/distributed/distributed-schema.yaml
@@ -91,6 +91,14 @@ properties:
 
               Works in conjunction with idle-timeout.
 
+          no-clients-timeout:
+            type:
+            - string
+            - "null"
+            description: |
+              Shut down the scheduler after this duration if no client heartbeats received,
+              and there are no running or queued tasks.
+
           work-stealing:
             type: boolean
             description: |
diff --git a/distributed/distributed.yaml b/distributed/distributed.yaml
index a7ec037e27c..4d77990357e 100644
--- a/distributed/distributed.yaml
+++ b/distributed/distributed.yaml
@@ -19,6 +19,7 @@ distributed:
     events-cleanup-delay: 1h
     idle-timeout: null       # Shut down after this duration, like "1h" or "30 minutes"
     no-workers-timeout: null # Shut down if there are tasks but no workers to process them
+    no-clients-timeout: null # Shut down after this duration of client inactivity, similar to idle-timeout
     work-stealing: True     # workers should steal tasks from each other
     work-stealing-interval: 100ms  # Callback time for work stealing
     worker-saturation: 1.1  # Send this fraction of nthreads root tasks to workers
diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index 0273d333da3..180a7aadd44 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -3582,6 +3582,8 @@ class Scheduler(SchedulerState, ServerNode):
     idle_timeout: float | None
     _no_workers_since: float | None  # Note: not None iff there are pending tasks
     no_workers_timeout: float | None
+    _no_clients_since: float
+    no_clients_timeout: float | None
 
     def __init__(
         self,
@@ -3597,6 +3599,7 @@ def __init__(
         security=None,
         worker_ttl=None,
         idle_timeout=None,
+        no_clients_timeout=None,
         interface=None,
         host=None,
         port=0,
@@ -3656,6 +3659,11 @@ def __init__(
             dask.config.get("distributed.scheduler.no-workers-timeout")
         )
         self._no_workers_since = None
+        self.no_clients_timeout = parse_timedelta(
+            no_clients_timeout
+            or dask.config.get("distributed.scheduler.no-clients-timeout")
+        )
+        self._no_clients_since = time()
 
         self.time_started = self.idle_since  # compatibility for dask-gateway
         self._replica_lock = RLock()
@@ -3934,6 +3942,9 @@ async def post(self):
         pc = PeriodicCallback(self._check_no_workers, 250)
         self.periodic_callbacks["no-workers-timeout"] = pc
 
+        pc = PeriodicCallback(self._check_no_clients, 250)
+        self.periodic_callbacks["no-clients-timeout"] = pc
+
         if extensions is None:
             extensions = DEFAULT_EXTENSIONS.copy()
             if not dask.config.get("distributed.scheduler.work-stealing"):
@@ -8521,6 +8532,36 @@ def check_idle(self) -> float | None:
                 self._ongoing_background_tasks.call_soon(self.close)
         return self.idle_since
 
+    def _check_no_clients(self) -> None:
+        """Shut down the schedule if there are no running tasks / no tasks ready to
+        run, and there hasn't been any client connection for
+        `distributed.scheduler.no-workers-timeout`."""
+        if self.status in (Status.closing, Status.closed):
+            return  # pragma: nocover
+
+        if (
+            self.queued
+            or self.unrunnable
+            or any(ws.processing for ws in self.workers.values())
+        ):
+            return
+
+        if self.jupyter:
+            self._no_clients_since = max(
+                self._no_clients_since,
+                self._jupyter_server_application.web_app.last_activity().timestamp(),
+            )
+        if self.clients:
+            clients_hb = max(c.last_seen for c in self.clients.values())
+            self._no_clients_since = max(self._no_clients_since, clients_hb)
+
+        if (
+            self.no_clients_timeout
+            and time() > self._no_clients_since + self.no_clients_timeout
+        ):
+            logger.info("No tasks and no client heartbeat; shutting scheduler down")
+            self._ongoing_background_tasks.call_soon(self.close)
+
     def _check_no_workers(self) -> None:
         """Shut down the scheduler if there have been tasks ready to run which have
         nowhere to run for `distributed.scheduler.no-workers-timeout`, and there
diff --git a/distributed/tests/test_scheduler.py b/distributed/tests/test_scheduler.py
index 9aaea1288a4..305364021d4 100644
--- a/distributed/tests/test_scheduler.py
+++ b/distributed/tests/test_scheduler.py
@@ -2541,6 +2541,36 @@ async def test_no_workers_timeout_processing(c, s, a, b):
         await asyncio.sleep(0.01)
 
 
+@pytest.mark.slow
+@gen_cluster(client=True)
+async def test_no_clients_timeout(c, s, a, b):
+    """Tests that with setting `no_clients_timeout` value, a submitted future
+    does complete, but afterwards cluster shuts down with the expected log message."""
+
+    beginning = time()
+    future = c.submit(slowinc, 1)
+    while not s.tasks:
+        await asyncio.sleep(0.01)
+    s.no_clients_timeout = 1.0
+    pc = PeriodicCallback(s._check_no_clients, 10)
+    pc.start()
+    await future
+
+    with captured_logger("distributed.scheduler") as logs:
+        start = time()
+        while s.status != Status.closed:
+            await asyncio.sleep(0.01)
+            assert time() < start + 3
+
+        start = time()
+        while not (a.status == Status.closed and b.status == Status.closed):
+            await asyncio.sleep(0.01)
+            assert time() < start + 1
+
+    assert "No tasks and no client heartbeat" in logs.getvalue()
+    pc.stop()
+
+
 @gen_cluster(client=True, config={"distributed.scheduler.bandwidth": "100 GB"})
 async def test_bandwidth(c, s, a, b):
     start = s.bandwidth