diff --git a/airflow/models/dag.py b/airflow/models/dag.py
index 5011b3ebb2b35d..ace9650f50f28c 100644
--- a/airflow/models/dag.py
+++ b/airflow/models/dag.py
@@ -57,6 +57,7 @@
 import re2
 import sqlalchemy_jsonfield
 from dateutil.relativedelta import relativedelta
+from packaging import version as packaging_version
 from sqlalchemy import (
     Boolean,
     Column,
@@ -116,6 +117,7 @@
     clear_task_instances,
 )
 from airflow.models.tasklog import LogTemplate
+from airflow.providers.fab import __version__ as FAB_VERSION
 from airflow.secrets.local_filesystem import LocalFilesystemBackend
 from airflow.security import permissions
 from airflow.settings import json
@@ -940,16 +942,26 @@ def update_old_perm(permission: str):
 
         updated_access_control = {}
         for role, perms in access_control.items():
-            updated_access_control[role] = updated_access_control.get(role, {})
-            if isinstance(perms, (set, list)):
-                # Support for old-style access_control where only the actions are specified
-                updated_access_control[role][permissions.RESOURCE_DAG] = set(perms)
+            if packaging_version.parse(FAB_VERSION) >= packaging_version.parse("1.3.0"):
+                updated_access_control[role] = updated_access_control.get(role, {})
+                if isinstance(perms, (set, list)):
+                    # Support for old-style access_control where only the actions are specified
+                    updated_access_control[role][permissions.RESOURCE_DAG] = set(perms)
+                else:
+                    updated_access_control[role] = perms
+                if permissions.RESOURCE_DAG in updated_access_control[role]:
+                    updated_access_control[role][permissions.RESOURCE_DAG] = {
+                        update_old_perm(perm)
+                        for perm in updated_access_control[role][permissions.RESOURCE_DAG]
+                    }
+            elif isinstance(perms, dict):
+                # Not allow new access control format with old FAB versions
+                raise AirflowException(
+                    "Please upgrade the FAB provider to a version >= 1.3.0 to allow "
+                    "use the Dag Level Access Control new format."
+                )
             else:
-                updated_access_control[role] = perms
-            if permissions.RESOURCE_DAG in updated_access_control[role]:
-                updated_access_control[role][permissions.RESOURCE_DAG] = {
-                    update_old_perm(perm) for perm in updated_access_control[role][permissions.RESOURCE_DAG]
-                }
+                updated_access_control[role] = {update_old_perm(perm) for perm in perms}
 
         return updated_access_control
 
diff --git a/tests/models/test_dag.py b/tests/models/test_dag.py
index d2b23c02654f31..831990fd68b1ec 100644
--- a/tests/models/test_dag.py
+++ b/tests/models/test_dag.py
@@ -2789,6 +2789,63 @@ def test_replace_outdated_access_control_actions(self):
         assert "permission is deprecated" in str(deprecation_warnings[0].message)
         assert "permission is deprecated" in str(deprecation_warnings[1].message)
 
+    @pytest.mark.parametrize(
+        "fab_version, perms, expected_exception, expected_perms",
+        [
+            pytest.param(
+                "1.2.0",
+                {
+                    "role1": {permissions.ACTION_CAN_READ, permissions.ACTION_CAN_EDIT},
+                    "role3": {permissions.RESOURCE_DAG_RUN: {permissions.ACTION_CAN_CREATE}},
+                    # will raise error in old FAB with new access control format
+                },
+                AirflowException,
+                None,
+                id="old_fab_new_access_control_format",
+            ),
+            pytest.param(
+                "1.2.0",
+                {
+                    "role1": [
+                        permissions.ACTION_CAN_READ,
+                        permissions.ACTION_CAN_EDIT,
+                        permissions.ACTION_CAN_READ,
+                    ],
+                },
+                None,
+                {"role1": {permissions.ACTION_CAN_READ, permissions.ACTION_CAN_EDIT}},
+                id="old_fab_old_access_control_format",
+            ),
+            pytest.param(
+                "1.3.0",
+                {
+                    "role1": {permissions.ACTION_CAN_READ, permissions.ACTION_CAN_EDIT},  # old format
+                    "role3": {permissions.RESOURCE_DAG_RUN: {permissions.ACTION_CAN_CREATE}},  # new format
+                },
+                None,
+                {
+                    "role1": {
+                        permissions.RESOURCE_DAG: {permissions.ACTION_CAN_READ, permissions.ACTION_CAN_EDIT}
+                    },
+                    "role3": {permissions.RESOURCE_DAG_RUN: {permissions.ACTION_CAN_CREATE}},
+                },
+                id="new_fab_mixed_access_control_format",
+            ),
+        ],
+    )
+    def test_access_control_format(self, fab_version, perms, expected_exception, expected_perms):
+        if expected_exception:
+            with patch("airflow.models.dag.FAB_VERSION", fab_version):
+                with pytest.raises(
+                    expected_exception,
+                    match="Please upgrade the FAB provider to a version >= 1.3.0 to allow use the Dag Level Access Control new format.",
+                ):
+                    DAG(dag_id="dag_test", schedule=None, access_control=perms)
+        else:
+            with patch("airflow.models.dag.FAB_VERSION", fab_version):
+                dag = DAG(dag_id="dag_test", schedule=None, access_control=perms)
+            assert dag.access_control == expected_perms
+
     def test_validate_executor_field_executor_not_configured(self):
         dag = DAG("test-dag", schedule=None)
         EmptyOperator(task_id="t1", dag=dag, executor="test.custom.executor")