We study the effect of an applied magnetic field on the resonant radiation from stacks of intrinsic Josephson junctions. We show that, when applying a moderate dc magnetic field in the plane of the junctions, a huge amplification of terahertz radiation can be obtained. This radiation enhancement occurs due to a modulation of the critical current. Furthermore, a dc magnetic field reducing the “radiation coupling” between junctions, produces a peculiar frequency-driven transition from stable to unstable terahertz radiation resonance.