With these caveats:
your MySQL version is correct (see the chart on the link that Wim posted)
you are using the proper ODBC driver to set up the data source. This depends on the platform used to query the source. If FM is on Windows, then the appropriate driver is used, for example.
your host (where the MySQL is being served) allows permission to access the database(s) remotely. Some ISP/hosts will only allow access within their own server/network. Usually this is a web application that they also host for dynamic websites. Or some hosting companies may grant limited access (read only, perhaps).
You need to get these questions answered by whomever is hosting the MySQL.
If all this seems too much, you may consider one of the fine FMP hosting companies. Many of these also have MySQL, should you have a website based on it. They can often give you connectivity between FM & MySQL.
-- sent from my iPhone4 --
If I have a remote access to mysql database,
are there any other limitations?
Do I need a MAC or Windows webserver, or is a standard LAMP webserver on Ubuntu / Linux ok?
Worldcloud offers ESS support and setup for FileMaker Server 11-13 for $2/ mth additional to a shared hosting plan...