It has been suggested that geochemical processes related to sea-ice growth and melt might be important for the polar carbon cycle via the so called sea-ice carbon pump (SICP). The SICP affects the air-sea CO2 exchange by influencing the composition of dissolved inorganic carbon (DIC) and total alkalinity (TA) in the surface ocean. Here we quantify the strength of the SICP-induced air-sea CO2 flux using the global three-dimensional ocean-sea-ice-biogeochemical model MPIOM/HAMOCC. Simulations prescribing the range of observed DIC and TA concentrations in the sea ice were performed under two idealized climate scenarios for the present-day and the future oceanic and sea-ice state, both forced with a fixed atmospheric CO2 concentration. Model results indicate that the SICP-induced air-sea CO2 uptake increases with higher ratios of TA:DIC prescribed in the sea ice relative to the basic oceanic TA:DIC ratios. Independent of the modeled scenario, the simulated strength of the SICP is larger in the Antarctic than in the Arctic, because of more efficient export of brine-associated DIC from the Antarctic mixed layer. On an annual basis, we generally find an enhanced SICP-induced oceanic CO2 uptake in regions with net sea-ice melt, and enhanced SICP-induced oceanic CO2 out-gassing in regions with net sea-ice growth. These general regional patterns are modified further by the blockage of air-sea gas exchange through sea-ice coverage. Integrated over the sea-ice zones of both hemispheres, the SICP-induced oceanic CO2 uptake ranges from 2 to 14 Tg C yr−1, which is up to 7% of the simulated net CO2 uptake in polar regions, but far less than 1% of the current global oceanic CO2 uptake. Hence, while we find that the SICP plays a minor role in the modern global carbon cycle, it is of importance for the regional carbon cycle at high latitudes.