Here we propose a magnetophotonic structure for the layer-selective magnetization switching with femtosecond laser pulses of different wavelengths. It is based on a chirped magnetophotonic crystal (MPC) containing magnetic GdFeCo and nonmagnetic dielectric layers. At each operating wavelength the laser pulses heat up to necessary level only one GdFeCo layer that leads to its magnetization reversal without any impact on the magnetization of the other layers. Moreover, magneto-optical reading of the MPC magnetization state is discussed. Lateral dimensions of the considered MPC can be made small enough to operate as a unit cell for data storage.