Fluid injections can induce aseismic slip, resulting in stress changes that may propagate faster than pore pressure diffusion, potentially triggering seismicity at substantial distances from injection wells. Constraining the maximum extent of these aseismic ruptures is, thus, important for better delineating the influence zone of injections concerning their seismic hazard. Here, we derive a scaling relation based on rupture physics for the maximum size of aseismic ruptures, accounting for fluid injections with arbitrary flow rate histories. Moreover, on the basis of mounting evidence that the moment release during these operations is often predominantly aseismic, we derive a scaling relation for the maximum magnitude of aseismic slip events. Our theoretical predictions are consistent with observations over a broad spectrum of event sizes, from laboratory to real-world cases, indicating that fault zone storativity, background stress change, and injected fluid volume are key determinants of the maximum size and magnitude of injection-induced slow slip events.