We present an analytical treatment of a two-dimensional (2D) magnetophotonic crystal (MPC) with a square lattice constructed from two infinite arrays of magnetoactive dielectric sheets at right angles, in the limit of very small sheet thickness and very high dielectric constant. Alteration of band structure by an external magnetic field is studied. Two different geometries are examined: the Faraday geometry—magnetic field parallel to the plane of 2D MPC—and the Voigt (Cotton-Mutton) geometry—magnetic field orthogonal to the plane of 2D MPC. In the case of Faraday geometry, we show that the optical activity reduces the symmetry of the system and removes degeneracy in the photonic band structure. Also, despite the weakness of magneto-optic activity, the dispersion ω(k) near band edges is strongly sensitive to external magnetic influence. In the vicinity of degeneracy, electromagnetic modes exhibit bistable behavior and discontinuously change their dispersion ω(k) when external magnetic field is applied. In the Voigt geometry s and p polarizations remain independent of each other, and only the band structure for s-polarized light is insignificantly altered.