We analyze a metal-dielectric structure composed of a silicon nanoparticle coupled to a stack of split-ring resonators, and reveal the possibility of optically-induced antiferromagnetic response of such a hybrid meta-molecule with a staggered pattern of the induced magnetization. We show that a hybrid metamaterial created by a periodic lattice of the meta-molecules supports antiferromagnetic modes with a checker-board pattern and the propagation of spin waves, opening new ways for manipulating artificial antiferromagnetism at high frequencies with low-loss materials.