diff --git a/moto/apigateway/models.py b/moto/apigateway/models.py
index fc2352e29..79295f231 100644
--- a/moto/apigateway/models.py
+++ b/moto/apigateway/models.py
@@ -1780,6 +1780,16 @@ class APIGatewayBackend(BaseBackend):
 
         return self.base_path_mappings[domain_name][base_path]
 
+    def delete_base_path_mapping(self, domain_name, base_path):
+
+        if domain_name not in self.domain_names:
+            raise DomainNameNotFound()
+
+        if base_path not in self.base_path_mappings[domain_name]:
+            raise BasePathNotFoundException()
+
+        self.base_path_mappings[domain_name].pop(base_path)
+
 
 apigateway_backends = {}
 for region_name in Session().get_available_regions("apigateway"):
diff --git a/moto/apigateway/responses.py b/moto/apigateway/responses.py
index ee890416f..6cdb22e5e 100644
--- a/moto/apigateway/responses.py
+++ b/moto/apigateway/responses.py
@@ -893,7 +893,7 @@ class APIGatewayResponse(BaseResponse):
                 )
                 return 200, {}, json.dumps(base_path_mapping)
             elif self.method == "DELETE":
-                # TODO Implements
-                pass
+                self.backend.delete_base_path_mapping(domain_name, base_path)
+                return 202, {}, ""
         except NotFoundException as e:
             return self.error("NotFoundException", e.message, 404)
diff --git a/tests/test_apigateway/test_apigateway.py b/tests/test_apigateway/test_apigateway.py
index 9cdff407b..dbb418ed1 100644
--- a/tests/test_apigateway/test_apigateway.py
+++ b/tests/test_apigateway/test_apigateway.py
@@ -2627,3 +2627,74 @@ def test_get_base_path_mapping_with_unknown_base_path():
     )
     ex.value.response["Error"]["Code"].should.equal("NotFoundException")
     ex.value.response["ResponseMetadata"]["HTTPStatusCode"].should.equal(404)
+
+
+@mock_apigateway
+def test_delete_base_path_mapping():
+    client = boto3.client("apigateway", region_name="us-west-2")
+    domain_name = "testDomain"
+    test_certificate_name = "test.certificate"
+    client.create_domain_name(
+        domainName=domain_name, certificateName=test_certificate_name
+    )
+
+    response = client.create_rest_api(name="my_api", description="this is my api")
+    api_id = response["id"]
+    base_path = "v1"
+    client.create_base_path_mapping(
+        domainName=domain_name, restApiId=api_id, basePath=base_path
+    )
+
+    client.get_base_path_mapping(domainName=domain_name, basePath=base_path)
+    response = client.delete_base_path_mapping(
+        domainName=domain_name, basePath=base_path
+    )
+    response["ResponseMetadata"]["HTTPStatusCode"].should.equal(202)
+
+    with pytest.raises(ClientError) as ex:
+        client.get_base_path_mapping(domainName=domain_name, basePath=base_path)
+
+    ex.value.response["Error"]["Message"].should.equal(
+        "Invalid base path mapping identifier specified"
+    )
+    ex.value.response["Error"]["Code"].should.equal("NotFoundException")
+    ex.value.response["ResponseMetadata"]["HTTPStatusCode"].should.equal(404)
+
+
+@mock_apigateway
+def test_delete_base_path_mapping_with_unknown_domain():
+    client = boto3.client("apigateway", region_name="us-west-2")
+
+    with pytest.raises(ClientError) as ex:
+        client.delete_base_path_mapping(domainName="unknown-domain", basePath="v1")
+
+    ex.value.response["Error"]["Message"].should.equal(
+        "Invalid domain name identifier specified"
+    )
+    ex.value.response["Error"]["Code"].should.equal("NotFoundException")
+    ex.value.response["ResponseMetadata"]["HTTPStatusCode"].should.equal(404)
+
+
+@mock_apigateway
+def test_delete_base_path_mapping_with_unknown_base_path():
+    client = boto3.client("apigateway", region_name="us-west-2")
+    domain_name = "testDomain"
+    test_certificate_name = "test.certificate"
+    client.create_domain_name(
+        domainName=domain_name, certificateName=test_certificate_name
+    )
+
+    response = client.create_rest_api(name="my_api", description="this is my api")
+    api_id = response["id"]
+    client.create_base_path_mapping(
+        domainName=domain_name, restApiId=api_id, basePath="v1"
+    )
+
+    with pytest.raises(ClientError) as ex:
+        client.delete_base_path_mapping(domainName=domain_name, basePath="unknown")
+
+    ex.value.response["Error"]["Message"].should.equal(
+        "Invalid base path mapping identifier specified"
+    )
+    ex.value.response["Error"]["Code"].should.equal("NotFoundException")
+    ex.value.response["ResponseMetadata"]["HTTPStatusCode"].should.equal(404)