Although carbon sequestration projects have yet to induce – or may never induce – a damaging earthquake, experiences from other deep injection industries such as hydraulic fracturing, enhanced geothermal systems, and saltwater disposal suggest that effective quantitative seismic risk assessment is appropriate for deep saline carbon sequestration (CCS) projects. One such imminent CCS project is the San Juan Basin CarbonSAFE Phase III program. The study detailed in this paper utilizes probabilistic geomechanical analyses combined with observations of the geological and operational parameters of the San Juan Basin to show that this project is of low induced seismic risk. The primary analysis is split into four sections. First, we assessed the literature for faults and past seismicity, and at least five faulting scenarios are directly relevant. Second, we developed and calibrated a mechanical earth model for the project site. Third, we performed Monte Carlo simulations considering reasonable uncertainties of the geomechanical parameters. Only the Hogback flexural faulting scenario presented high Coulomb failure functions, but fourth, we determined the risk to be low based on the combined lack of historical seismicity, geological framework of the flexural faults, and the presence of saltwater injection at the same depth as the proposed supercritical carbon dioxide injection. In order to assess the likelihood of inducing slip on the basement faults, an analytical treatment of the poroelastic stress perturbations from the proposed injection was considered, and this also suggested a low chance for triggering or inducing earthquakes at this depth. The most sensitive parameters in the geomechanical calculations were the dip and the coefficient of friction. The least sensitive were the strike and the orientation of the maximum horizontal principal stress. In summary, results of this study suggest that the San Juan Basin CarbonSAFE project is unlikely to induce a medium- or large-scale event.