In a warming climate, surface meltwater production on large ice sheets is expected to increase. If this water is delivered to the ice sheet base it may have important consequences for ice dynamics. For example, basal water distributed in a diffuse network can decrease basal friction(1,2) and accelerate ice flow(3-8), whereas channelized basal water can move quickly to the ice margin, where it can alter fjord circulation and submarine melt rates(9,10). Less certain is whether surface meltwater can be trapped and stored in subglacial lakes beneath large ice sheets. Here we show that a subglacial lake in Greenland drained quickly, as seen in the collapse of the ice surface, and then refilled from surface meltwater input. We use digital elevation models from stereo satellite imagery and airborne measurements to resolve elevation changes during the evolution of the surface and basal hydrologic systems at the Flade Isblink ice cap in northeast Greenland. During the autumn of 2011, a collapse basin about 70 metres deep and about 0.4 cubic kilometres in volume formed near the southern summit of the ice cap as a subglacial lake drained into a nearby fjord. Over the next two years, rapid uplift of the floor of the basin (which is approximately 8.4 square kilometres in area) occurred as surface meltwater flowed into crevasses around the basin margin and refilled the subglacial lake. Our observations show that surface meltwater can be trapped and stored at the bed of an ice sheet. Sensible and latent heat released by this trapped meltwater could soften nearby colder basal ice(11) and alter downstream ice dynamics(12,13). Heat transport associated with meltwater trapped in subglacial lakes should be considered when predicting how ice sheet behaviour will change in a warming climate.