I have a Java app using a MySQL database through hibernate. The database is really used as persistence layer: The database is read at the initial load of the program, and
Or change both applications so the Java app is truly the owner of the MySQL database and exposes it as a service. You're coupling the two apps at the database level by doing what you're proposing.
If you have one owner of the data you can hide schema changes and such behind the service interface. You can also make it possible to have a publish/subscribe mechanism to alert interested parties about database changes. If those things are important to you, I'd reconsider letting another application access MySQL directly.