The study focuses on the removal of dissolved oxygen from a model monoethanolamine (MEA)-based absorbent to prevent oxidative degradation during the absorption process of flue gas CO2 removal. A mathematical model was developed to evaluate the deoxygenation parameters in a gas-liquid membrane contactor using composite hollow-fiber membranes with a thin non-porous layer made of a blend of polytrimethylsilylpropyne and polyvinyltrimethylsilane. The modeling results were shown to be in good agreement with experimental data on O2 removal efficiency. The model was applied to assess the scaling of the membrane system for dissolved O2 removal to handle an absorbent flow rate of 120 m3/h in a hypothetical CO2 capture plant using absorption technology. The influence of system parameters (absorbent linear flow rate, membrane contactor length, number of membranes in the contactor, initial O2 concentration in the absorbent) on O2 removal efficiency was determined. It was shown that to achieve 90% removal of dissolved oxygen, at least 12 membrane modules with a length of 1 meter and a total membrane area of 1800 m2 are required. Various scenarios of dynamically changing external system parameters (oxygen concentration in the feed, absorbent flow rate) were simulated for the designed membrane system to predict the system’s response.