Carbonate mineral production and dissolution regulate atmospheric carbon dioxide (CO2) concentrations via modulation of the ocean alkalinity content. The anthropogenic rise in atmospheric CO2 reduces calcification rates and enhances calcium carbonate dissolution, which increases ocean alkalinity, counteracts acidification, and stimulates ocean CO2 uptake. However, carbonate dissolution takes place primarily in the deep ocean, so this feedback is slow, maintaining ocean CO2 uptake over millennial timescales. Here we present evidence that seawater alkalinity concentrations on the continental shelf are increasing on annual-decadal timescales, at a rate that is orders of magnitude faster than the deep ocean feedback. Biogeochemical model analyses suggest this fast feedback results from calcium carbonate dissolution in the shelf seafloor driven by increasing atmospheric CO2 concentrations. Earth-system modelling indicates that shelf carbonate dissolution has been accelerating since the 1800s and may account for up to 30% of the missing ~0.3 Pg C yr-1 in ocean model carbon budgets.