Exciton-polaritons of a hybrid type, emerging in a structure comprising semimagnetic (Mn-doped) and nonmagnetic quantum wells coupled via the microcavity optical mode are demonstrated and studied. Thanks to the susceptibility of the excitons in the magnetic quantum well to the magnetic field, all the emerging hybrid polariton states acquire magnetic properties. In that way, external magnetic field enables control over the degree of hybridization, tuning of the ratio of the excitonic to photonic components of the hybrid polaritons, and alteration of the direction and dynamics of the energy transfer between the excitonic states in magnetic and nonmagnetic quantum wells. The presented possibility of the hybridization of a semimagnetic exciton with an exciton in a material that itself does not exhibit any meaningful magnetic effects is highly promising in the context of the fabrication of-to date lacking-organic, perovskite, or dichalcogenide-based systems with strong magnetooptical properties.