What is the maximum number of tables that MySQL can handle?
The fact that you are asking this question is probably an indicator that you are not taking a best practice approach to your problem.
One potential situation where you could need a lot of tables is when you are developing multi-tenant application where for each tenant you create separate set of tables (let's say with tentantId as a table name prefix). See this article (part Data Isolation): http://www.javacodegeeks.com/2013/11/architecting-a-multi-tenant-application.html