diff --git a/airflow/jobs/scheduler_job.py b/airflow/jobs/scheduler_job.py
index 0b0463713e29f..d0831adb6496f 100644
--- a/airflow/jobs/scheduler_job.py
+++ b/airflow/jobs/scheduler_job.py
@@ -1696,10 +1696,18 @@ def _schedule_dag_run(
             and dag.dagrun_timeout
             and dag_run.start_date < timezone.utcnow() - dag.dagrun_timeout
         ):
-            dag_run.state = State.FAILED
-            dag_run.end_date = timezone.utcnow()
-            self.log.info("Run %s of %s has timed-out", dag_run.run_id, dag_run.dag_id)
+            dag_run.set_state(State.FAILED)
+            unfinished_task_instances = (
+                session.query(TI)
+                .filter(TI.dag_id == dag_run.dag_id)
+                .filter(TI.execution_date == dag_run.execution_date)
+                .filter(TI.state.in_(State.unfinished))
+            )
+            for task_instance in unfinished_task_instances:
+                task_instance.state = State.SKIPPED
+                session.merge(task_instance)
             session.flush()
+            self.log.info("Run %s of %s has timed-out", dag_run.run_id, dag_run.dag_id)
 
             # Work out if we should allow creating a new DagRun now?
             self._update_dag_next_dagruns([session.query(DagModel).get(dag_run.dag_id)], session)
diff --git a/tests/jobs/test_scheduler_job.py b/tests/jobs/test_scheduler_job.py
index ac5a837d7c4d2..097317087e9f2 100644
--- a/tests/jobs/test_scheduler_job.py
+++ b/tests/jobs/test_scheduler_job.py
@@ -23,6 +23,7 @@
 import unittest
 from datetime import timedelta
 from tempfile import NamedTemporaryFile, mkdtemp
+from time import sleep
 from unittest import mock
 from unittest.mock import MagicMock, patch
 from zipfile import ZipFile
@@ -3813,6 +3814,68 @@ def test_do_schedule_max_active_runs_upstream_failed(self):
         ti = run2.get_task_instance(task1.task_id, session)
         assert ti.state == State.QUEUED
 
+    def test_do_schedule_max_active_runs_dag_timed_out(self):
+        """Test that tasks are set to a finished state when their DAG times out"""
+
+        dag = DAG(
+            dag_id='test_max_active_run_with_dag_timed_out',
+            start_date=DEFAULT_DATE,
+            schedule_interval='@once',
+            max_active_runs=1,
+            catchup=True,
+        )
+        dag.dagrun_timeout = datetime.timedelta(seconds=1)
+
+        with dag:
+            task1 = BashOperator(
+                task_id='task1',
+                bash_command=' for((i=1;i<=600;i+=1)); do sleep "$i";  done',
+            )
+
+        session = settings.Session()
+        dagbag = DagBag(
+            dag_folder=os.devnull,
+            include_examples=False,
+            read_dags_from_db=True,
+        )
+
+        dagbag.bag_dag(dag=dag, root_dag=dag)
+        dagbag.sync_to_db(session=session)
+
+        run1 = dag.create_dagrun(
+            run_type=DagRunType.SCHEDULED,
+            execution_date=DEFAULT_DATE,
+            state=State.RUNNING,
+            session=session,
+        )
+        run1_ti = run1.get_task_instance(task1.task_id, session)
+        run1_ti.state = State.RUNNING
+
+        sleep(1)
+
+        run2 = dag.create_dagrun(
+            run_type=DagRunType.SCHEDULED,
+            execution_date=DEFAULT_DATE + timedelta(seconds=10),
+            state=State.RUNNING,
+            session=session,
+        )
+
+        dag.sync_to_db(session=session)
+
+        job = SchedulerJob(subdir=os.devnull)
+        job.executor = MockExecutor()
+        job.processor_agent = mock.MagicMock(spec=DagFileProcessorAgent)
+
+        _ = job._do_scheduling(session)
+
+        assert run1.state == State.FAILED
+        assert run1_ti.state == State.SKIPPED
+        assert run2.state == State.RUNNING
+
+        _ = job._do_scheduling(session)
+        run2_ti = run2.get_task_instance(task1.task_id, session)
+        assert run2_ti.state == State.QUEUED
+
     def test_do_schedule_max_active_runs_task_removed(self):
         """Test that tasks in removed state don't count as actively running."""