not "directly", but perhaps indirectly if both are web published with PHP (or any web that can communicate with both databases).
As beverly suggests this is really dependent on what you have on the MySQL side. If you have some sort of web based interface to the MySQL database with a decent API you might be able to use a plugin and cURL or the actual PHP API built into FileMaker.
or just the xml queries and any web app that can process the XML (no need to use the FileMaker API for PHP classes)
Get the CWP (custom web publishing) Guide (PDF)