We report the fabrication and performance of an annular, cryogenic, phonon-mediated veto detector that can host an inner target detector, allowing substantial reduction in radiogenic backgrounds for rare event search experiments. A germanium veto detector of mass ∼500 g with an outer diameter of 76 mm and an inner diameter of 28 mm was produced inside of which was mounted a 25 mm diameter germanium inner target detector of mass ∼10 g. The detector was designed using inputs from a GEANT4 based simulation, where it was modeled to be sandwiched between two germanium detectors. The simulation showed that the background rates (dominated by gamma interactions) could be reduced by > 90%, and that such an arrangement is sufficient for aggressive background reduction needed for neutrino and dark matter search experiments. Operating at mK temperatures at the experimental site, the veto detector prototype achieved a baseline resolution of 1.24 ± 0.02 keV while hosting a functional inner target detector. The baseline resolution of the inner target detector was 147 ± 2 eV. The experimental results of an identical detector arrangement are in excellent agreement with the simulation.