The glaciological significance of ice shelves is relatively well established for the stability of modern ice sheets of Antarctica. Past ice shelves of the Arctic, however, are poorly documented while their role for the stability of former ice sheets remains mostly unknown. Here we present swath bathymetry data and seismostratigraphic profiles that reveal a large moraine system extending along the continental slope off Baffin Island, demonstrating that a 500-m thick ice shelf covered northern Baffin Bay during the last glacial episode. We suggest that this ice shelf had a profound impact on the stability of a series of major ice streams that drained the interior of the Laurentide, Innuitian and Greenland ice sheets. Climate warming and global sea-level rise in the early stage of deglaciation possibly contributed to a large-scale break-up of the ice shelf, which led to the destabilisation and reorganisation of tributary ice streams from these three ice sheets.