As the global climate warms, increased surface meltwater production on ice shelves may trigger ice-shelf collapse and enhance global sea-level rise. The formation of surface rivers could help prevent ice-shelf collapse if they can efficiently evacuate meltwater. Here, we present observations of the evolution of a surface river into an ice-shelf estuary atop the Petermann Ice Shelf in northwest Greenland, and identify a second estuary at the nearby Ryder Ice Shelf. This surface hydrology process can foster fracturing and enhance calving. At the Petermann estuary, sea ice was observed converging at the river mouth upstream, indicating a flow reversal. Seawater persists in the estuary, after the surrounding icescape is frozen. Along the base of Petermann estuary, linear fractures were initiated at the calving front and propagated upstream along the channel. Similar fractures along estuary channels shaped past large rectilinear calving events at the Petermann and Ryder Ice Shelves. Increased surface melting in a warming world will enhance fluvial incision, promoting estuary development, longitudinal fracturing orthogonal to ice-shelf fronts, and increase rectilinear calving. Estuaries could develop in Antarctica within the next half-century, resulting in increased calving and accelerating both ice loss and global sea-level rise.