Shelves have been estimated to account for more than one-fifth of the global marine primary production. It has been also conjectured that shelves strongly influence the oceanic absorption of anthropogenic CO2 (carbon shelf pump). Owing to their coarse resolution, currently applied global climate models are inappropriate to investigate the impact of climate change on shelves and regional models do not account for the complex interaction with the adjacent open ocean. In this study, a global ocean general circulation model and biogeochemistry model were set up with a distorted grid providing a maximal resolution for the NW European shelf and the adjacent northeast Atlantic. Using model climate projections we found that already a~moderate warming of about 2.0 K of the sea surface is linked with a reduction by ~ 30% of the biological production on the NW European shelf. If we consider the decline of anthropogenic riverine eutrophication since the 1990s, the reduction of biological production amounts is even larger. The relative decline of NW European shelf productivity is twice as strong as the decline in the open ocean (~ 15%). The underlying mechanism is a spatially well confined stratification feedback along the continental shelf break. This feedback reduces the nutrient supply from the deep Atlantic to about 50%. In turn, the reduced productivity draws down CO2 absorption in the North Sea by ~ 34% at the end of the 21st century compared to the end of the 20th century implying a strong weakening of shelf carbon pumping. Sensitivity experiments with diagnostic tracers indicate that not more than 20% of the carbon absorbed in the North Sea contributes to the long-term carbon uptake of the world ocean. The rest remains within the ocean's mixed layer where it is exposed to the atmosphere. The predicted decline in biological productivity, and decrease of phytoplankton concentration (in the North Sea by averaged 25%) due to reduced nutrient imports from the deeper Atlantic will probably affect the local fish stock negatively and therefore fisheries in the North Sea.