Climate‐induced changes in the physical, chemical, and biological environment are expected to increasingly stress marine ecosystems, with important consequences for fisheries exploitation. Here, we use the APECOSM‐E numerical model (Apex Predator ECOSystem Model ‐ Estimation) to evaluate the future impacts of climate change on the physiology, spatial distribution, and abundance of skipjack tuna, the worldwide most fished species of tropical tuna. The main novelties of our approach lie in the mechanistic link between environmental factors, metabolic rates, and behavioral responses and in the fully three dimensional representation of habitat and population abundance. Physical and biogeochemical fields used to force the model are provided by the last generation of the IPSL‐CM5 Earth System Model run from 1990 to 2100 under a ‘business‐as‐usual’ scenario (RCP8.5). Our simulations show significant changes in the spatial distribution of skipjack tuna suitable habitat, as well as in their population abundance. The model projects deterioration of skipjack habitat in most tropical waters and an improvement of habitat at higher latitudes. The primary driver of habitat changes is ocean warming, followed by food density changes. Our projections show an increase of global skipjack biomass between 2010 and 2050 followed by a marked decrease between 2050 and 2095. Spawning rates are consistent with population trends, showing that spawning depends primarily on the adult biomass. On the other hand, growth rates display very smooth temporal changes, suggesting that the ability of skipjack to keep high metabolic rates in the changing environment is generally effective. Uncertainties related to our model spatial resolution, to the lack or simplification of key processes and to the climate forcings are discussed.