The Altiplano-Puna Magma Body (APMB) in the Central Andes is the largest imaged magma reservoir on Earth, and is located within the second highest orogenic plateau on Earth, the Altiplano-Puna. Although the APMB is a first-order geologic feature similar to the Sierra Nevada batholith, its role in the surface uplift history of the Central Andes remains uncertain. Here we show that a long-wavelength topographic dome overlies the seismically measured extent of the APMB, and gravity data suggest that the uplift is isostatically compensated. Isostatic modelling of the magmatic contribution to dome growth yields melt volumes comparable to those estimated from tomography, and suggests that the APMB growth rate exceeds the peak Cretaceous magmatic flare-up in the Sierran batholith. Our analysis reveals that magmatic addition may provide a contribution to surface uplift on par with lithospheric removal, and illustrates that surface topography may help constrain the magnitude of pluton-scale melt production.