Physical absorption is a potential technology for economic carbon capture due to its low energy consumption, however, the absorption efficiency of current systems must be improved. In this study, novel hybrid absorption/stripping membrane contactors (HASMCs) for physical solvent carbon capture are proposed. The simultaneous absorption and stripping within one module provides instant regeneration of the solvent and results in the enhancement of absorption. HASMCs with parallel-flow and cross-flow configurations and using empty or spacer-filled channels are investigated by rigorous computational fluid dynamics simulation. The internal profiles of transmembrane mass fluxes reveal that cross-flow HASMCs are much more effective than the parallel-flow ones and the modules using spacer-filled channels give better performance than the ones using empty channels. The mass transfer coefficients of HASMCs are much higher than predicted by correlations in the literature.