We report a study on the remanent magnetization M r induced by field cooling across the ordering temperature T N in antiferromagnetic CoO nanoparticles with different sizes. The nanoparticles are composed by a structurally and magnetically ordered core and a structurally ordered and magnetically disordered shell with a thickness of about 2 nm. The ordered core has cell parameters, moments direction, and modulus similar to those of bulk CoO. M r is shown to be proportional to the cooling field H cool . The low-temperature saturation values of M r ͓M r ͑0͔͒ in the CoO nanoparticles are about two orders of magnitude higher than those found for bulk CoO. M r / M r ͑0͒ of CoO nanoparticles scales with temperature in a single curve, independently on the magnitude of H cool and on nanoparticles size, except for temperatures near to T N since T N is size dependent.