We demonstrate that transitions between Zeeman-split sublevels of Rb atoms are resonantly induced by the motion of the atoms (velocity: about 100 m/s) in a periodic magnetostatic field (period: 1 mm) when the Zeeman splitting corresponds to the frequency of the magnetic field experienced by the moving atoms. A circularly polarized laser beam polarizes Rb atoms with a velocity selected using the Doppler effect and detects their magnetic resonance in a thin cell, to which the periodic field is applied with the arrays of parallel current-carrying wires.