CO2 mineralization is an alternative to conventional geological storage and results in permanent carbon storage as a solid, with no need for long-term monitoring and no requirements for significant energy input. Novel technologies for carbon dioxide capture and mineralization involve the use of gas-liquid membrane contactors for post-combustion capture. The scope of the present study is to investigate the application of hollow fiber membrane contactor technology for combined CO2 capture from energy-intensive industry flue gases and CO2 mineralization, in a single-step multiphase process. The process is also a key enabler of the circular economy for the cement industry, a major contributor in global industrial CO2 emissions, as CaCO3 particles, obtained through the mineralization process, can be directed back into the cement production as fillers for partially substituting cement in high-performance concrete. High CO2 capture efficiency is achieved, as well as CaCO3 particles of controlled size and crystallinity are synthesized, in every set of operating parameters employed. The intensified gas-liquid membrane process is assessed by calculating an overall process mass transfer coefficient accounting for all relevant mass transfer resistances and the enhanced mass transfer due to reactive conditions on the shell side. The obtained nanocomposite particles have been extensively characterized by DLS, XRD, TGA, SEM, TEM, and FTIR studies, revealing structured aggregates (1–2 μm average aggregate size) consisting of cubic calcite when the contactor mode is employed.