diff --git a/moto/apigateway/models.py b/moto/apigateway/models.py
index 95eaad7ad..c729b1d31 100644
--- a/moto/apigateway/models.py
+++ b/moto/apigateway/models.py
@@ -1610,7 +1610,7 @@ class APIGatewayBackend(BaseBackend):
         if integration_type in ["AWS", "AWS_PROXY"] and not re.match("^arn:aws:", uri):
             raise InvalidArn()
         if integration_type in ["AWS", "AWS_PROXY"] and not re.match(
-            "^arn:aws:apigateway:[a-zA-Z0-9-]+:[a-zA-Z0-9-]+:(path|action)/", uri
+            "^arn:aws:apigateway:[a-zA-Z0-9-]+:[a-zA-Z0-9-.]+:(path|action)/", uri
         ):
             raise InvalidIntegrationArn()
         integration = resource.add_integration(
diff --git a/tests/test_apigateway/test_apigateway_integration.py b/tests/test_apigateway/test_apigateway_integration.py
index e9ec6033a..16156b4ae 100644
--- a/tests/test_apigateway/test_apigateway_integration.py
+++ b/tests/test_apigateway/test_apigateway_integration.py
@@ -166,6 +166,23 @@ def test_aws_integration_dynamodb_multiple_resources():
     )
 
 
+@mock_apigateway
+def test_aws_integration_sagemaker():
+    region = "us-west-2"
+    client = boto3.client("apigateway", region_name=region)
+    sagemaker_endpoint = "non-existing"
+    integration_action = f"arn:aws:apigateway:{region}:runtime.sagemaker:path//endpoints/{sagemaker_endpoint}/invocations"
+
+    api_id, resource_id = create_integration_test_api(client, integration_action)
+
+    # We can't invoke Sagemaker
+    # Just verify that the integration action was successful
+    response = client.get_integration(
+        restApiId=api_id, resourceId=resource_id, httpMethod="PUT"
+    )
+    response.should.have.key("uri").equals(integration_action)
+
+
 def create_table(dynamodb, table_name):
     # Create DynamoDB table
     dynamodb.create_table(