Due to the advantages of good fracture performance and the application of carbon capture and storage (CCS), supercritical carbon dioxide (SC-CO₂) is considered a promising alternative for hydraulic fracturing. However, the fracture initiation mechanism and its propagation under pressurized SC-CO₂ jet are still unknown. To address these problems, a fluid–structure interaction (FSI)-based numerical simulation model along with a user-defined code was used to investigate the fracture initiation in an inhomogeneous shale rock. The mechanism of fracturing under the effect of SC-CO₂ jet was explored, and the effects of various influencing factors were analyzed and discussed. The results indicated that higher velocity jets of SC-CO₂ not only caused hydraulic-fracturing ring, but also resulted in the increase of stress in the shale rock. It was found that, with the increase of perforation pressure, more cracks initiated at the tip. In contrast, the length of cracks at the root decreased. The length-to-diameter ratio and the aperture ratio distinctly affected the pressurization of SC-CO₂ jet, and contributed to the non-linear distribution and various maximum values of the stress in shale rock. The results proved that Weibull probability distribution was appropriate for analysis of the fracture initiation. The studied parameters explain the distribution of weak elements, and they affect the stress field in shale rock.