Yes Facebook supports oembed. You can checkout the documentation here..
https://developers.facebook.com/docs/plugins/oembed-endpoints
Note: In order to make this API work properly with ajax calls on mobile devices; You need to use the endpoint domain "apps.facebook.com" instead of "www.facebook.com":
https://apps.facebook.com/plugins/post/oembed.json/?url={content-url}
This is because if you use the endpoint that is provided in the official documentation "www.facebook.com" the User agent of the mobile devices will force the redirect to "m.facebook.com" which does not have this endpoint implemented.