The annual growth rates in Swedish forests are higher than the annual harvest rates, and this has resulted in high rates of carbon sequestration in the Swedish forestry sector. Any factor that tends to reduce growth rates also has the potential to reduce forest carbon sequestration rates, and ozone may be one such factor. The aim of this study was to estimate to what extent the occurrence of elevated tropospheric ozone concentrations can negatively affect carbon sequestration by Swedish forest ecosystems. The net primary production (NPP) of Swedish forests was simulated, using the 3-PG model, for representative forest stands in six different geographical zones across Sweden, with and without assumed negative impacts of ozone. Ozone impacts were derived from dose-response relationships, calculated from open-top chamber experiments with young trees. The results of the 3-PG simulations showed that the NPP was generally higher in the A2 and B2 Intergovernmental Panel on Climate Change (IPCC) future climate scenarios, as compared to the current climate, for all tree species and in all geographical zones across Sweden. Biomass production was reduced by 4.3‐15.5% for conifers (Norway spruce (Picea abies L) and Scots pine (Pinus sylvestris L) and by 1.4‐4.3% for birch (Betula pendula Roth and Betula pubescence Ehrh) under ambient ozone conditions as compared to the preindustrial ozone level. The greatest reduction in biomass was found in southern Sweden. Biomass was reduced by similar percentage value in future climate scenarios as that in the current climate.