The dependences of the exciton-polariton photoluminescence spectra on the intensity of optical excitation and external magnetic fields are investigated in cylindrical mesas based on high-quality microcavities. It was found that with an increase of the intensity of optical excitation above a certain threshold at sufficiently large magnetic field or with an increase of magnetic fields at constant optical excitation, the distribution of exciton-polaritons over Zeeman sublevels becomes substantially non-Boltzmannian.