Combinations of nontrivial band topology and long-range magnetic order hold promise for realizations of novel spintronic phenomena, such as the quantum anomalous Hall effect and the topological magnetoelectric effect. Following theoretical advances, material candidates are emerging. Yet, so far a compound that combines a band-inverted electronic structure with an intrinsic net magnetization remains unrealized. MnBi_{2}Te_{4} has been established as the first antiferromagnetic topological insulator and constitutes the progenitor of a modular (Bi_{2}Te_{3})_{n}(MnBi_{2}Te_{4}) series. Here, for n=1, we confirm a nonstoichiometric composition proximate to MnBi_{4}Te_{7}. We establish an antiferromagnetic state below 13 K followed by a state with a net magnetization and ferromagnetic-like hysteresis below 5 K. Angle-resolved photoemission experiments and density-functional calculations reveal a topologically nontrivial surface state on the MnBi_{4}Te_{7}(0001) surface, analogous to the nonmagnetic parent compound Bi_{2}Te_{3}. Our results establish MnBi_{4}Te_{7} as the first band-inverted compound with intrinsic net magnetization providing a versatile platform for the realization of magnetic topological states of matter.