Around the periphery of the Greenland ice sheet, Global Navigation Satellite System (GNSS) stations record uplift, reflecting Earth’s response to past and recent unloading of ice mass. On the southeast coast, near the Kangerlussuaq glacier, GNSS stations show abnormally rapid ground uplift exceeding 12 mm/yr. Current earth deformation models, which employ a layered Earth structure, cannot explain this rapid uplift. We find that 3D models that incorporate a “track” of weakened earth structure, consistent with the passage of Greenland over the Iceland plume, can explain the rapid uplift of southeast Greenland. This uplift is dominated by a viscous response that is accelerated by the low viscosities of the hot plume track. Recent mass loss, occurring during the last millennium and especially within the past few decades, drives most of the uplift. By contrast, uplift due to more ancient deglaciation was exhausted soon after the last ice age, and thus does not contribute significantly today. This rapid viscous response, occurring above regions of weakened mantle, is not usually considered in glacial isostatic adjustment models, but it can affect ice-ocean interactions, and thus retreat rates, of marine terminating glaciers. Such regions will become increasingly important in the near future as deglaciation accelerates.