We investigate the effect of strong magnetic fields on the adiabatic radial oscillations of hadronic stars. We describe magnetized hadronic matter within the framework of the relativistic nonlinear Walecka model and integrate the equations of relativistic radial oscillations to determine the fundamental pulsation mode. We consider that the magnetic field increases, in a density dependent way, from the surface, where it has a typical magnetar value of 1015G, to the interior of the star, where it can be as large as 3×1018G. We show that magnetic fields of the order of 1018G at the stellar core produce a significant change in the frequency of neutron star pulsations with respect to unmagnetized objects. If radial pulsations are excited in magnetar flares, they can leave an imprint in the flare lightcurves and open a new window for the study of highly magnetized ultradense matter.