MySQL 5.6 Reference Manual Including MySQL NDB Cluster 7.3-7.4 Reference Guide
MySQL has no limit on the number of databases. The underlying file system may have a limit on the number of directories.
MySQL has no limit on the number of tables. The underlying file
system may have a limit on the number of files that represent
tables. Individual storage engines may impose engine-specific
constraints. InnoDB
permits up to 4 billion
tables.