Azure API Management currently supports OpenAPI versions 1.2 and 2.0. Microsoft is in the process of adding support for the recently released OpenAPI version 3 of the specification in both JSON and YAML formats.
The OpenAPI Specification (formerly known as Swagger) defines a standard, programming language-agnostic interface description for REST APIs. Microsoft's work is based on the OpenAPI.NET SDK open source project.
To vote and share your thoughts on this development, please see OpenAPI v3 support in Azure API Management.