We present the results of experiments on the local magnetization reversal of artificial magnetic skyrmions in a Co/Pt multilayer film with a perpendicular magnetization by a magnetic force microscope (MFM) probe. The sample was a Co/Pt film containing an array of cylindrical regions with reduced anisotropy, modified by a focused He+ ion beam. The magnetic state of the sample was monitored by magnetic force microscopy. The magnetization reversal was performed by the MFM probe field during passes over the sample at low altitudes. The effects of the interaction of the field of the MFM probe with the skyrmion state of magnetization in these structures are investigated by micromagnetic simulation.