Anthropogenic fluid injection into the subsurface is known to produce induced seismicity. Well-known examples include enhanced geothermal systems, wastewater disposal and hydraulic fracturing. Efforts to quantify induced-seismicity risk and to develop mitigation strategies are hampered by a dearth of numerical schemes that can accommodate realistic Earth models while capturing the full spectrum of applicable physics. Here, we present a new 3D stochastic approach to modelling induced seismicity, whereby three possible triggering mechanisms are accounted for. Uncertainties in input parameters are addressed stochastically to provide a probabilistic assessment of induced-seismicity risk. Fault models can be constructed from 3D seismic data or can be randomly generated each iteration based on known regional characteristics. Regions of modelled faults that exceed the assigned failure criteria are mapped and provide estimates for the magnitudes of any seismic events that may occur. In this manner, we can estimate the probabilities of generating an event of a certain magnitude based on the modelled injection scenario and parameter distributions. Due to the stochastic approach, probabilities for the expected maximum magnitudes of events and the sensitivities of results to the different input parameters can be analyzed. This type of modelling can be used to give a site-specific assessment of how the probability of generating an induced event changes, based on different treatment designs. Ultimately, our work aims to significantly reduce the financial, environmental and social risk of induced seismicity, as well as the potential to cause damage to local populations and infrastructure.