We show by first-principles calculations that the magnetic moments of zigzag ZnO nanoribbons can be efficiently modulated by transverse electric fields. Depending on the field direction, the total magnetic moment in a zigzag ZnO nanoribbon can be remarkably enhanced or reduced and even completely quenched with increasing field over a threshold strength. However, in weak electric fields below the threshold, the magnetic moment in the zigzag ZnO nanoribbons nearly remains unchanged, which can be explained in terms of intrinsic transverse electric polarization and quantum confinement effects. The threshold electric field required to modulate the magnetic moment decreases significantly with increasing ribbon width, showing practical importance.