We have investigated the electrical transport properties of Dirac electrons in a monolayer graphene sheet in the presence of a perpendicular magnetic field that is weakly and periodically modulated along one direction. We find that the Landau levels broaden into bands and their width oscillates as a function of the band index and the magnetic field. We determine the ${\ensuremath{\sigma}}_{yy}$ component of the magnetoconductivity tensor for this system, which is shown to exhibit Weiss oscillations. We also analytically determine the asymptotic expressions for ${\ensuremath{\sigma}}_{yy}$. We compare these results to recently obtained results for electrically modulated graphene, as well as those for a magnetically modulated conventional two-dimensional electron gas (2DEG) system. We find that in the magnetically modulated graphene system considered in this work, Weiss oscillations in ${\ensuremath{\sigma}}_{yy}$ have a reduced amplitude compared to that in the 2DEG but are less damped by temperature, while they have a higher amplitude than in the electrically modulated graphene system. We also find that these oscillations are out of phase by $\ensuremath{\pi}$ with those of the electrically modulated system while they are in phase with those in the 2DEG system.