The behaviour of a magneto-optically active biological-like medium under picosecond optical excitation is analysed. The new technique is based on the fact that photons trapped in multiple scattering events inside the magneto-optical medium leave the medium with larger induced rotation angles, as they travel longer distances. Two- and three-dimensional displacements of the photons in the medium are separately analysed. The dependence of this effect on the applied magnetic field strength, the value of the magneto-optical constant of the medium and the standard deviation of the statistical distribution of the photons scattered inside the turbid medium are studied. The best values for the magnetic field and optical parameters of the biological medium are proposed for the experimental observation of the picosecond magneto-optical phenomena in scattering media of biological origin. We also make some prospective studies to evaluate the potential application of the magneto-optical effect as a tool for optical tissue biopsy. Values for the optimum magnetic field intensities and for the expected experimental sensitivity in diverse conditions are reported.