Oceanic uptake and long‐term storage of atmospheric carbon dioxide (CO₂) are strongly driven by the marine "biological pump," i.e., sinking of biotically fixed inorganic carbon and nutrients from the surface into the deep ocean (Sarmiento and Bender, 1994; Volk and Hoffert, 1985). Sinking velocity of marine particles depends on seawater viscosity, which is strongly controlled by temperature (Sharqawy et al., 2010). Consequently, marine particle flux is accelerated as ocean temperatures increase under global warming (Bach et al., 2012). Here we show that this previously overlooked "viscosity effect" could have profound impacts on marine biogeochemical cycling and carbon uptake over the next centuries to millennia. In our global warming simulation, the viscosity effect accelerates particle sinking by up to 25%, thereby effectively reducing the portion of organic matter that is respired in the surface ocean. Accordingly, the biological carbon pump's efficiency increases, enhancing the sequestration of atmospheric CO₂ into the ocean. This effect becomes particularly important on longer time scales when warming reaches the ocean interior. At the end of our simulation (4000 A.D.), oceanic carbon uptake is 17% higher, atmospheric CO₂ concentration is 180 ppm lower, and the increase in global average surface temperature is 8% weaker when considering the viscosity effect. Consequently, the viscosity effect could act as a long‐term negative feedback mechanism in the global climate system.