diff --git a/moto/apigateway/exceptions.py b/moto/apigateway/exceptions.py
index a3dd86083..5df362a20 100644
--- a/moto/apigateway/exceptions.py
+++ b/moto/apigateway/exceptions.py
@@ -215,5 +215,5 @@ class MethodNotFoundException(NotFoundException):
 
     def __init__(self):
         super(MethodNotFoundException, self).__init__(
-            "NotFoundException", "Invalid method properties specified"
+            "NotFoundException", "Invalid Method identifier specified"
         )
diff --git a/moto/apigateway/models.py b/moto/apigateway/models.py
index 75541664c..cebf6df5a 100644
--- a/moto/apigateway/models.py
+++ b/moto/apigateway/models.py
@@ -343,6 +343,9 @@ class Resource(CloudFormationModel):
             raise MethodNotFoundException()
         return method
 
+    def delete_method(self, method_type):
+        self.resource_methods.pop(method_type)
+
     def add_integration(
         self,
         method_type,
@@ -1118,6 +1121,10 @@ class APIGatewayBackend(BaseBackend):
         method = resource.get_method(method_type)
         return method.apply_operations(patch_operations)
 
+    def delete_method(self, function_id, resource_id, method_type):
+        resource = self.get_resource(function_id, resource_id)
+        resource.delete_method(method_type)
+
     def get_authorizer(self, restapi_id, authorizer_id):
         api = self.get_rest_api(restapi_id)
         authorizer = api.authorizers.get(authorizer_id)
diff --git a/moto/apigateway/responses.py b/moto/apigateway/responses.py
index e91a10c4f..ad24706e2 100644
--- a/moto/apigateway/responses.py
+++ b/moto/apigateway/responses.py
@@ -180,8 +180,11 @@ class APIGatewayResponse(BaseResponse):
         method_type = url_path_parts[6]
 
         if self.method == "GET":
-            method = self.backend.get_method(function_id, resource_id, method_type)
-            return 200, {}, json.dumps(method)
+            try:
+                method = self.backend.get_method(function_id, resource_id, method_type)
+                return 200, {}, json.dumps(method)
+            except NotFoundException as nfe:
+                return self.error("NotFoundException", nfe.message)
         elif self.method == "PUT":
             authorization_type = self._get_param("authorizationType")
             api_key_required = self._get_param("apiKeyRequired")
diff --git a/tests/test_apigateway/test_apigateway.py b/tests/test_apigateway/test_apigateway.py
index 3d7c77a2b..c8e77cd0b 100644
--- a/tests/test_apigateway/test_apigateway.py
+++ b/tests/test_apigateway/test_apigateway.py
@@ -463,6 +463,32 @@ def test_create_method_response():
     response.should.equal({"ResponseMetadata": {"HTTPStatusCode": 200}})
 
 
+@mock_apigateway
+def test_delete_method():
+    client = boto3.client("apigateway", region_name="us-west-2")
+    response = client.create_rest_api(name="my_api", description="this is my api")
+    api_id = response["id"]
+
+    resources = client.get_resources(restApiId=api_id)
+    root_id = [resource for resource in resources["items"] if resource["path"] == "/"][
+        0
+    ]["id"]
+
+    client.put_method(
+        restApiId=api_id, resourceId=root_id, httpMethod="GET", authorizationType="none"
+    )
+
+    client.get_method(restApiId=api_id, resourceId=root_id, httpMethod="GET")
+
+    client.delete_method(restApiId=api_id, resourceId=root_id, httpMethod="GET")
+
+    with pytest.raises(ClientError) as ex:
+        client.get_method(restApiId=api_id, resourceId=root_id, httpMethod="GET")
+    err = ex.value.response["Error"]
+    err["Code"].should.equal("NotFoundException")
+    err["Message"].should.equal("Invalid Method identifier specified")
+
+
 @mock_apigateway
 def test_integrations():
     client = boto3.client("apigateway", region_name="us-west-2")