Because of the critically stressed nature of the upper crust, the injection of large volumes of carbon dioxide (CO2) into shallow geological reservoirs can trigger seismicity and induce ground deformations when the injection increases the fluid pressure in the vicinity of potentially seismic faults. The increased fluid pressure reduces the strength against fault slip, allowing the stored elastic energy to be released in seismic events that can produce felt ground accelerations. Here, we seek to explore the likelihood ground motions induced by a CO2 injection using hydromechanical modelling with multiphase fluid flow and dynamic rupture, including fault-frictional weakening. We extend the previous work of Cappa and Rutqvist, in which activation of a normal fault at critical stress may be possible for fast rupture nucleating by localized increase in fluid pressure and large decrease in fault friction. In this paper, we include seismic wave propagation generated by the rupture. For our assumed system and injection rate, simulations show that after a few days of injection, a dynamic fault rupture of few centimetres nucleates at the base of the CO2 reservoir and grows bilaterally, both toward the top of the reservoir and outside. The rupture is asymmetric and affects a larger zone below the reservoir where the rupture is self-propagating (without any further pressure increase) as a result of fault-strength weakening. The acceleration and deceleration of the rupture generate waves and result in ground accelerations (∼0.1–0.6 g) consistent with observed ground motion records. The maximum ground acceleration is obtained near the fault, and horizontal accelerations are generally markedly higher than vertical accelerations.