Ice sheets are currently ignored in global methane budgets. Although ice sheets have been proposed to contain large reserves of methane that may contribute to a rise in atmospheric methane concentration if released during periods of rapid ice retreat, no data exist on the current methane footprint of ice sheets. Here we find that subglacially produced methane is rapidly driven to the ice margin by the efficient drainage system of a subglacial catchment of the Greenland ice sheet. We report the continuous export of methane-supersaturated waters (CH4(aq)) from the ice-sheet bed during the melt season. Pulses of high CH4(aq) concentration coincide with supraglacially forced subglacial flushing events, confirming a subglacial source and highlighting the influence of melt on methane export. Sustained methane fluxes over the melt season are indicative of subglacial methane reserves that exceed methane export, with an estimated 6.3 tonnes (discharge-weighted mean; range from 2.4 to 11 tonnes) of CH4(aq) transported laterally from the ice-sheet bed. Stable-isotope analyses reveal a microbial origin for methane, probably from a mixture of inorganic and ancient organic carbon buried beneath the ice. We show that subglacial hydrology is crucial for controlling methane fluxes from the ice sheet, with efficient drainage limiting the extent of methane oxidation to about 17 per cent of methane exported. Atmospheric evasion is the main methane sink once runoff reaches the ice margin, with estimated diffusive fluxes (4.4 to 28 millimoles of CH4 per square metre per day) rivalling that of major world rivers. Overall, our results indicate that ice sheets overlie extensive, biologically active methanogenic wetlands and that high rates of methane export to the atmosphere can occur via efficient subglacial drainage pathways. Our findings suggest that such environments have been previously underappreciated and should be considered in Earth’s methane budget.