The Antarctic Ice Sheet (AIS) remains the largest uncertainty in projections of future sea level rise. A likely climate‐driven vulnerability of the AIS is thinning of floating ice shelves resulting from surface‐melt‐driven hydrofracture or incursion of relatively warm water into subshelf ocean cavities. The resulting melting, weakening, and potential ice shelf collapse reduces shelf buttressing effects. Upstream ice flow accelerates, causing thinning, grounding‐line retreat, and potential ice sheet collapse. While high‐resolution projections have been performed for localized Antarctic regions, full‐continent simulations have typically been limited to low‐resolution models. Here we quantify the vulnerability of the entire present‐day AIS to regional ice shelf collapse on millennial timescales treating relevant ice flow dynamics at the necessary ∼1‐km resolution. A collapse of any of the ice shelves dynamically connected to the West Antarctic Ice Sheet (WAIS) is sufficient to trigger ice sheet collapse in marine‐grounded portions of the WAIS. Vulnerability elsewhere appears limited to localized responses.