We develop a general computational approach, based on the discrete dipole approximation, for the study of radiation dynamics near or inside an object with arbitrary linear dielectric permittivity, and magnetic permeability tensors. Our method can account for dispersion and losses and provides insight on the role of local-field corrections in discrete magnetodielectric structures. We illustrate our method in the case of a source inside a magneto-dielectric, isotropic sphere for which the spontaneous emission rate of a source can be computed analytically. We show that our approach is in excellent agreement with the exact result, providing an approach capable of handling both the electric and magnetic response of advanced metamaterials