diff --git a/moto/mq/exceptions.py b/moto/mq/exceptions.py
index d22dc58fd..a3d83deab 100644
--- a/moto/mq/exceptions.py
+++ b/moto/mq/exceptions.py
@@ -52,21 +52,6 @@ class UnknownUser(MQError):
         return json.dumps(body)
 
 
-class UnsupportedEngineType(MQError):
-    def __init__(self, engine_type: str):
-        super().__init__("BadRequestException", "")
-        self.engine_type = engine_type
-
-    def get_body(
-        self, *args: Any, **kwargs: Any
-    ) -> str:  # pylint: disable=unused-argument
-        body = {
-            "errorAttribute": "engineType",
-            "message": f"Broker engine type [{self.engine_type}] does not support configuration.",
-        }
-        return json.dumps(body)
-
-
 class UnknownEngineType(MQError):
     def __init__(self, engine_type: str):
         super().__init__("BadRequestException", "")
diff --git a/moto/mq/models.py b/moto/mq/models.py
index 579c66910..393a3bb80 100644
--- a/moto/mq/models.py
+++ b/moto/mq/models.py
@@ -12,7 +12,6 @@ from .exceptions import (
     UnknownBroker,
     UnknownConfiguration,
     UnknownUser,
-    UnsupportedEngineType,
     UnknownEngineType,
 )
 
@@ -236,14 +235,7 @@ class Broker(BaseModel):
                 console_access=user.get("consoleAccess", False),
             )
 
-        if self.engine_type.upper() == "RABBITMQ":
-            self.configurations: Optional[Dict[str, Any]] = None
-        else:
-            current_config = configuration or {
-                "id": f"c-{mock_random.get_random_hex(6)}",
-                "revision": 1,
-            }
-            self.configurations = {"current": current_config, "history": []}
+        self.configurations: Dict[str, Any] = {"current": configuration, "history": []}
         if self.engine_type.upper() == "RABBITMQ":
             console_url = f"https://0000.mq.{region}.amazonaws.com"
             endpoints = ["amqps://mockmq:5671"]
@@ -290,8 +282,8 @@ class Broker(BaseModel):
         if auto_minor_version_upgrade is not None:
             self.auto_minor_version_upgrade = auto_minor_version_upgrade
         if configuration:
-            self.configurations["history"].append(self.configurations["current"])  # type: ignore[index]
-            self.configurations["current"] = configuration  # type: ignore[index]
+            self.configurations["history"].append(self.configurations["current"])
+            self.configurations["current"] = configuration
         if engine_version:
             self.engine_version = engine_version
         if host_instance_type:
@@ -386,7 +378,7 @@ class MQBackend(BaseBackend):
         authentication_strategy: str,
         auto_minor_version_upgrade: bool,
         broker_name: str,
-        configuration: Dict[str, Any],
+        configuration: Optional[Dict[str, Any]],
         deployment_mode: str,
         encryption_options: Dict[str, Any],
         engine_type: str,
@@ -402,6 +394,15 @@ class MQBackend(BaseBackend):
         tags: Dict[str, str],
         users: List[Dict[str, Any]],
     ) -> Tuple[str, str]:
+        if configuration is None:
+            # create default configuration
+            default_config = self.create_configuration(
+                name=f"{broker_name}-configuration",
+                engine_type=engine_type,
+                engine_version=engine_version,
+                tags={},
+            )
+            configuration = {"id": default_config.id, "revision": 1}
         broker = Broker(
             name=broker_name,
             account_id=self.account_id,
@@ -471,9 +472,7 @@ class MQBackend(BaseBackend):
     def create_configuration(
         self, name: str, engine_type: str, engine_version: str, tags: Dict[str, str]
     ) -> Configuration:
-        if engine_type.upper() == "RABBITMQ":
-            raise UnsupportedEngineType(engine_type)
-        if engine_type.upper() != "ACTIVEMQ":
+        if engine_type.upper() not in ["ACTIVEMQ", "RABBITMQ"]:
             raise UnknownEngineType(engine_type)
         config = Configuration(
             account_id=self.account_id,
diff --git a/tests/test_mq/test_mq.py b/tests/test_mq/test_mq.py
index 85724a456..4bd3c299c 100644
--- a/tests/test_mq/test_mq.py
+++ b/tests/test_mq/test_mq.py
@@ -25,6 +25,11 @@ def test_create_broker_minimal():
     assert "BrokerId" in resp
     assert resp["BrokerArn"].startswith("arn:aws")
 
+    # Should create default Configuration, if not specified
+    broker = client.describe_broker(BrokerId=resp["BrokerId"])
+    assert "Current" in broker["Configurations"]
+    assert "Id" in broker["Configurations"]["Current"]
+
 
 @mock_mq
 def test_create_with_tags():
@@ -269,7 +274,6 @@ def test_describe_multiple_rabbits():
         == "https://0000.mq.us-east-2.amazonaws.com"
     )
     assert len(resp["BrokerInstances"][0]["Endpoints"]) == 1
-    assert "Configurations" not in resp
     assert resp["Logs"] == {"General": False}
     assert len(resp["SubnetIds"]) == 4
 
diff --git a/tests/test_mq/test_mq_configuration.py b/tests/test_mq/test_mq_configuration.py
index cba2f04da..8e52caa69 100644
--- a/tests/test_mq/test_mq_configuration.py
+++ b/tests/test_mq/test_mq_configuration.py
@@ -35,22 +35,6 @@ def test_create_configuration_minimal():
     assert revision["Revision"] == 1
 
 
-@mock_mq
-def test_create_configuration_for_rabbitmq():
-    client = boto3.client("mq", region_name="us-east-1")
-
-    with pytest.raises(ClientError) as exc:
-        client.create_configuration(
-            EngineType="RABBITMQ", EngineVersion="rabbit1", Name="myconfig"
-        )
-    err = exc.value.response["Error"]
-    assert err["Code"] == "BadRequestException"
-    assert (
-        err["Message"]
-        == "Broker engine type [RABBITMQ] does not support configuration."
-    )
-
-
 @mock_mq
 def test_create_configuration_for_unknown_engine():
     client = boto3.client("mq", region_name="us-east-1")