Climate change projections to the year 2100 may miss physical-biogeochemical feedbacks that emerge later from the cumulative effects of climate warming. In a coupled climate simulation to the year 2300, the westerly winds strengthen and shift poleward, surface waters warm, and sea ice disappears, leading to intense nutrient trapping in the Southern Ocean. The trapping drives a global-scale nutrient redistribution, with net transfer to the deep ocean. Ensuing surface nutrient reductions north of 30 degrees S drive steady declines in primary production and carbon export (decreases of 24 and 41%, respectively, by 2300). Potential fishery yields, constrained by lower-trophic-level productivity, decrease by more than 20% globally and by nearly 60% in the North Atlantic. Continued high levels of greenhouse gas emissions could suppress marine biological productivity for a millennium.