We demonstrate a novel all-dielectric magnetophotonic structure that consists of two-dimensional arrays of bismuth substituted iron-garnet nanocylinders supporting both localized (Fabry–Perot-like) and lattice (guided-like) optical modes. Simultaneous excitation of the two kinds of modes provides a significant enhancement of the Faraday effect by 3 times and transverse magneto-optical Kerr effect by an order of magnitude compared to the smooth magnetic film of the same effective thickness. Both magneto-optical effects are boosted in wide spectral and angular ranges making the nanocylinder array magnetic dielectric structures promising for applications with short and tightly focused laser pulses.