Understanding the physical mechanisms which link fluid injection with triggered earthquakes is critical in minimizing hazard in subsurface fluid‐injection operations. Currently, injection‐induced changes in effective stress on faults are considered as the main criterion in triggering seismic fault slip. However, rate of change in effective stress, together with inertial effects, are also be implicated in this criterion. We present a modified critical stiffness criterion to investigate the relative likelihood of triggering earthquakes during injection for different injection rate schedules (constant‐vs‐cycled‐vs‐increasing). A stability analysis of fault stress is used to define a critical stiffness as a function of magnitudes and rate of change in effective stresses. The relative potential for triggering earthquakes due to fluid injection is investigated using a coupled fluid‐flow‐deformation model. Polarities of change in critical stiffness are employed as an index to define the tendency for a transition from aseismic to seismic reactivation. During constant rate injection and self‐equilibration stages, the absolute magnitude of effective stress controls the transition. Conversely, the rate of change in effective stress dominates this transition when injection suddenly starts or stops, and inertial effects suppress the transformation to seismic slip. Cycling injection rates into a given fault is the most stable, followed by constant injection, with linear injection the least stable for the same total volume injected. High permeability reservoirs and strike‐slip faulting regimes reduce the potential of inducing seismicity. This work provides both new insights into assessing the seismic risks associated with injection and guidance for mitigation.