Transport in three-dimensional topological insulators relies on the existence of a spin-momentum locked surface state that encloses the insulating bulk. In this work we show how, in a topological insulator p-n junction, a magnetic field turns this surface state into an electronic Mach-Zehnder interferometer. Transmission of the junction can be tuned from zero to unity, resulting in virtually perfect visibility of the interference pattern, and the reflected and transmitted currents carry opposite spin polarization so that the junction also acts as a spin filter. Our setup therefore realizes a novel and highly tunable spintronic device where the effects of spin-momentum locking in topological insulator surface states can be probed directly in a transport experiment.