Using ab initio density functional calculations, we show that pentagonal and hexagonal nanotubes of Ge can be stabilized in the antiprism structure by doping with Mn atoms. In both cases the infinite nanotubes are metallic and ferromagnetic. Hexagonal nanotubes have the highest average magnetic moments of 3.06 $\mu$B per Mn atom found so far in metal doped nanotubes of semiconductors, while the pentagonal nanotubes show a transition from a ferromagnetic to a ferrimagnetic state upon compression with an abrupt change in the magnetic moments, leading to the possibility of these nanotubes to act as a nano-piezomagnet.