We propose a new model for the cracking of cement paste induced by carbonation. Carbonation is the reaction of cement paste with CO2, resulting in its mineralisation into CaCO3. This is a ubiquitous phenomenon that occurs naturally or is engineered to decrease CO2 equivalent emissions. Carbonation is well known to result in the acidification of concrete pore solution, which triggers corrosion of steel reinforcement. Another effect that has received far less attention is carbonation-induced cracking, to which modern blended cements are significantly more susceptible. Thus, predicting carbonation-induced cracking is important for durability predictions of concrete infrastructure and for unlocking the potential of novel CO2 mineralisation technologies. However, the existing literature on this topic is very limited. We present a coupled model that captures state-of-the-art knowledge of the involved chemo-mechanical processes, including CO2 transport through cement paste, cement paste shrinkage, and induced cracking simulated with a phase-field fracture model. A novel model has been developed to describe the transport of CO2 through emerging cracks, allowing the impact of crack width on CO2 transport through each crack to be considered. The model has been implemented in COMSOL Multiphysics software and solved numerically using the finite element method. Due to the scarcity of data on carbonation-induced shrinkage and crack width, an experimental study was conducted on CEM II/L A paste samples at water-to-cement ratios of 0.4, 0.5 and 0.6. The numerical model was found to capture the experimentally observed carbonation-induced cracking pattern and surface crack width accurately. Modelling results indicate that carbonation-induced cracking has a strong impact on the carbonation rate. The model also reveals that considering the transition zone between fully and non-carbonated zones is essential for capturing carbonation-induced cracking.