We studied, using the spin density functional theory, the manganese mononitride (MnN) grown on GaN in the wurtzite phase, forming the GaN/MnN heterostructures. We obtained a ferromagnetic ground state with a higher magnetic moment than the hypothetical wurtzite bulk MnN. This behavior can be explained in terms of the high magnetization of the MnN interface monolayers that have longer first and second neighbors bond lengths due to structure relaxation. We suggest that this system can be applied to the new spintronics technology by being able to provide spin polarized carriers in the important wide-gap nitride systems.882