I’ve followed a recipe found on rcgroups.com. In short: you can run MissionPlanner (MP) in Ubuntu with mono.

Once you’ve installed mono and extracted the zip file with MP, you start it with:

$ mono MissionPlanner.exe

The only thing that wasn’t in the recipe, was that you need to give rights to your user in order to get the rights to communicate with the drone (in my case: APM 2.5):

$ sudo adduser USERNAME dialout