We propose a novel type of hybrid metal-dielectric structures composed of silicon nanoparticles and split-ring resonators for advanced control of optically induced magnetic response. We reveal that a hybrid "metamolecule" may exhibit a strong distance-dependent magnetic interaction that may flip the magnetization orientation and support "antiferromagnetic" ordering in a hybrid metamaterial created by a periodic lattice of such metamolecules. The propagation of magnetization waves in the hybrid structures opens new ways for manipulating artificial "antiferromagnetic" ordering at high frequencies.