The injection‐induced slip of a fault containing along‐the‐fault geometrical complexities such as permeable cracks, dilational jogs and branches, was studied numerically using a plane‐strain hydraulic fracture model. The fault is modeled by placing complexities evenly spaced on either side of the inlet where fluid coming from a steady source is injected at a constant rate. The fault slip obeys the Coulomb friction law with slip weakening of the coefficient of friction. The applied shear stress is less than the residual fault strength, corresponding to a situation where a fault undergoes stable slip behind a slowly advancing rupture front. The numerical results show that the segments of complexity may not only delay slip zone extension and fluid flow, but temporarily increase slip rates. Short‐term faster slip rates occur after cracks and jogs are pressurized. The slip rate can reach values typical of microearthquake events, accompanied by rising and then dropping pressure and producing a stress release. Especially, the discontinuous slip sources are separated by the right‐angle jogs that do not slip. The slip on branches can be activated by fluid invasion and an associated normal effective stress reduction, and the slow slip sources eventually move from the fault to the branches. Even if a hydraulic fracturing treatment presents a low risk of generating dynamic slip, when fractures intersect faults containing geometrical complexities, fast slip events may be induced. The spatiotemporally varying slip rates and patterns presented provide an alternative interpretation for recorded seismic slip signals.