The dynamical dielectric response function and collective excitations of a twodimensional electron gas under a perpendicular magnetic field and in the presence of an additional weak unidirectional spatially modulated periodic magnetic field are calculated within the random-phase approximation It is found that the dynamical dielectric response function is not only broadened by the additional magnetic modulation, but it also contains a series of subsingularities at the band edges. Such broadening of the response function is also found to modify the magnetoplasmon modes of such a system over their unmodulated counterpart. The origin of the new subsingularities is attributed to the magnetic modulation-induced broadening of the energy spectrum. This broadening, being non-uniform, leads to the reintroduction of particle-hole excitations into the dielectric response function. Such fine structures at the band edges are similar in appearance to those recently reported for the case of a weak unidirectional spatially modulated periodic electric potential though however the former may be up to about an order of magnitude larger in bandwidth compared to those seen for the electric case when equal modulation strengths are considered. It is therefore proposed that these new predicted fine structures should be more readily observed in far-infrared spectroscopy experiments over their electric counterpart.