Android does not support MySQL out of the box. The “normal” way to access your database would be to put a Restful server in front of it and use the HTTPS protocol to connect to the Restful front end.
Have a look at ContentProvider. It is normally used to access a local database (SQLite) but it can be used to get data from any data store.
I do recommend that you look at having a local copy of all/some of your websites data locally, that way your app will still work when the Android device hasn’t got a connection. If you go down this route then a service can be used to keep the two databases in sync.