The magnetic properties of black phosphorene nanoribbons are investigated using static and dynamical mean-field theory. Besides confirming the existence of ferromagnetic/antiferromagnetic edge magnetism, our detailed calculations using large unit cells find a phase transition at weak interaction strength to an incommensurate (IC) magnetic phase. A detailed Fourier analysis of the magnetization patterns in the IC phase shows the existence of a second critical interaction strength, where the incommensurate phase changes to an antiferromagnetic (AFM) or ferromagnetic (FM) phase. We demonstrate that the difference of the ground-state energies of the AFM and FM phase is exponentially small, making it possible to switch between both states by a small external field. Finally, we analyze the influence of strain and disorder on the magnetic properties and show that while the IC phase is robust to Anderson type disorder, it is fragile against strain.