Apache::Session is somewhat misnamed -- you don't need to use Apache/mod_perl to use the module. It stores the information in whatever storage mechanism you think is appropriate (filesystem, database, DBM), and not in memory -- although you can use a memory storage (like IPC::Shareable or something) if you're feeling lucky and industrious.

In your case, it would be MySQL. If you're using CGI, then you're going to need to open up a database handle for each request. Various other schemes exist based on whatever sort of server process you're using. The module has some decent documentation, check it out: Apache::Session.