You would need to create Java Runtime Environment for the Wii (no easy task). Also minecraft runs like poo even on a decent computer, I think it would kill a wii.
Edit: I guess there is an open source version of Java now (OpenJDK), so get porting.
btw i feel this a good time to remind you guys that sea of thieves was made by rare, who also made DKC1-3 and DK64, alongside banjo kazooie and conker's bad fur day