Polydimethylsiloxane is a translucent silicone material present in most lab-on-a-chip devices. In membrane technology, polydimethylsiloxane provides a separation barrier for various applications such as oxygenation, vapor recovery and nanofiltration. The easy-to-use combination of silicon and crosslinker and its properties make it widely applicable for two-dimensional device geometries. Here we develop a new sacrificial lithography technique to produce three-dimensional membrane geometries using rapid prototyping. The three-dimensional PDMS membranes are applied for gas–liquid-contacting. The membrane geometries are based on triple-periodic minimal surface TPMS structures, which are inaccessible via currently available membrane fabrication methods. The novel membrane geometries display superior mass transport of CO2 through PDMS into water compared with computational fluid dynamics simulations of state-of-the-art hollow-fiber membranes of equal geometry parameters. In addition, we further advance the membrane geometry to a cylindrical shaped contactor device for oxygenation.