Well, there are a number of different ways you could achieve it. You could put it in an i-frame; you could open the calender within php and skim the contents; or you could even set up a soap server on the machine with the MySQL database and then a client on the other and use SOAP to get the info.
I'd probably do it such that I have a page on the machine with the MySQL database which when called builds and outputs an xml file. The page on the other machine can then call this page, get the xml content and handle it any way it wants to. This method allows more control at the final end but without going OTT (doing it with SOAP would be a little silly really :p).
HTH
Bubble