Outlet glaciers grounded on a bed that deepens inland and extends below sea level are potentially vulnerable to 'marine ice sheet instability'. This instability, which may lead to runaway ice loss, has been simulated in models, but its consequences have not been directly observed in geological records. Here we provide new surface-exposure ages from an outlet of the East Antarctic Ice Sheet that reveal rapid glacier thinning occurred approximately 7,000 years ago, in the absence of large environmental changes. Glacier thinning persisted for more than two and a half centuries, resulting in hundreds of metres of ice loss. Numerical simulations indicate that ice surface drawdown accelerated when the otherwise steadily retreating glacier encountered a bedrock trough. Together, the geological reconstruction and numerical simulations suggest that centennial-scale glacier thinning arose from unstable grounding line retreat. Capturing these instability processes in ice sheet models is important for predicting Antarctica's future contribution to sea level change.