The underground injection and geological sequestration of carbon dioxide (CO₂) is a promising approach for reducing the levels of CO₂ in the atmosphere. To mitigate the leakage of CO₂ resulting from natural fracture networks in rock masses, the sequestration process is commonly accompanied by the injection of reactive Portland cement representing a coupled hydro-chemo-mechanical process. In this work, a numerical approach based on the unified pipe network method (UPM) is presented that considers the coupled permeation and diffusion processes with chemical precipitation. Most input parameters are derived from the published literature. The proposed approach is validated through a comparison with analytical solutions, which are applied to simulate the CO₂ sequestration process in a fractured rock mass. The results indicate that the long-term sequestration effect, which is highly influenced by the fracture distribution, can be captured effectively by the model. Consequently, the presented approach can assist engineers in properly designing the arrangement of boreholes and determining the concentration of the grouting material.