If you just want to run .class
files without much concern for performance, you could create a bytecode interpreter, which might be simpler than porting / creating a full compiler. You can find the format of these class files detailed here, and the behavior of the VM specified here.
You'll also need to pick a runtime -- OpenJDK and GNU Classpath are probably the best bets -- and port it to MINIX by implementing its native
methods in C. native
methods are usually concerned with platform-specific stuff, like calls to file I/O, and therefore cannot be implemented in the platform-independent Java language.
There are a number of other links and resources that you might find useful on this wiki page.