The seismic hazard of a fault system is controlled by the maximum possible earthquake magnitude it can host. However, existing methods to estimate maximum magnitudes can result in large uncertainties or ignore their temporal evolution. Here, we show how the maximum possible earthquake magnitude of a fault system can be assessed by combining high-resolution fault coupling maps with a physics-based model from three-dimensional dynamic fracture mechanics confirmed by dynamic rupture simulations. We demonstrate the method on the Anninghe-Zemuhe fault system in southwestern China, where dense near-fault geodetic data has been acquired. Our results show that this fault system currently has the potential to generate Mw7.0 earthquakes with maximum magnitudes increasing to Mw7.3 by 2200. These results are supported by the observed rupture extents and recurrence times of historical earthquakes and the b values of current seismicity. Our work provides a practical way to assess the earthquake potential of natural faults.