Sea ice in the Southern Ocean has expanded over most of the past 20 y, but the decline in sea ice since 2016 has taken experts by surprise. This recent evolution highlights the poor performance of numerical models for predicting extent and thickness, which is due to our poor understanding of ice dynamics. Ocean waves are known to play an important role in ice break-up and formation. In addition, as ocean waves decay, they cause a stress that pushes the ice in the direction of wave propagation. This wave stress could not previously be quantified due to insufficient observations at large scales. Sentinel-1 synthetic aperture radars (SARs) provide high-resolution imagery from which wave height is measured year round encompassing Antarctica since 2014. Our estimates give an average wave stress that is comparable to the average wind stress acting over 50 km of sea ice. We further reveal highly variable half-decay distances ranging from 400 m to 700 km, and wave stresses from 0.01 to 1 Pa. We expect that this variability is related to ice properties and possibly different floe sizes and ice thicknesses. A strong feedback of waves on sea ice, via break-up and rafting, may be the cause of highly variable sea-ice properties.