The effect of external magnetic fields on two radiative (band-to-band and on-site) recombination channels in II-VI dilute magnetic semiconductors and related nanostructures has been considered. The 3d on-site emission of manganese ions in CdMgTe matrices containing periodic inclusions of CdMnTe narrow-band-gap layers with thicknesses of 0.5, 1.5, and 3.0 monolayers has been investigated in magnetic fields of up to 6 T. It has been shown that, in a magnetic field, luminescence of manganese ions weakens because of the decrease in the rate of spin-dependent excitation transfer from band states to the Mn2+ 3d shell. The maximum suppression of 3d luminescence has been observed in the matrix with a CdMnTe layer 3.0 monolayers thick. This indicates that the main factor responsible for the energy transfer is the internal field near the CdMnTe layers, which determines the magnetic splitting and spin polarization of band states.