We demonstrate experimentally a new type of order in optical magnetism resembling the staggered structure of spins in antiferromagnetic ordered materials. We study hybrid electromagnetic metasurfaces created by assembling hybrid meta-atoms formed by metallic split-ring resonators and dielectric particles with a high refractive index, both supporting optically-induced magnetic dipole resonances of different origin. Each pair (or ‘metamolecule’) is characterized by two interacting magnetic dipole moments with the distance-dependent magnetization resembling the spin exchange interaction in magnetic materials. By directly mapping the structure of the electromagnetic fields, we demonstrate experimentally that strong coupling between the optically-induced magnetic moments of different origin can flip the magnetisation orientation in a metamolecule creating an antiferromagnetic lattice of staggered optically-induced magnetic moments in hybrid metasurfaces.