In this work, we investigate the magneto-optical absorption in a phosphorene monolayer subjected to a perpendicular static magnetic field. The magneto-optical absorption power is calculated using the projection operator technique taking account of the effect of electron – optical phonon interaction. Numerical results showed that in the case of absence of any interaction, the higher the resonant frequency, the smaller absorbed power was. If the electron - phonon interaction exists, there appear the cyclotron-phonon resonant peaks which show the electron transitions between Landau levels by absorbing a photon accompanied by absorbing/emitting an optical phonon. The obtained results are important for further studies and applications of the phosphorene based structures in optoelectronic devices.