The Altiplano-Puna ultralow-velocity zone in the central Andes, South America, is the largest active magma body in Earth's continental crust. Space geodetic observations reported an uplift in the Altiplano-Puna proper at a rate of similar to 10 mm/year; however, the nature of the inferred inflation source has been uncertain. We present data showing that the uplift has persisted at a nearly constant rate over the past two decades, and is surrounded by a broad zone of subsidence. We show that the ongoing uplift and peripheral subsidence may result from a large mid-crustal diapir fed by partial melt from the Altiplano-Puna Magma Body.