Fast radio bursts (FRBs) are millisecond transient astrophysical phenomena and bright at radio frequencies. The emission mechanism, however, remains unsolved yet. One scenario is a coherent emission associated with the magnetar flares and resulting relativistic shock waves. Here, we report unprecedentedly large-scale simulations of relativistic magnetized ion-electron shocks, showing that strongly linear-polarized electromagnetic waves are excited. The kinetic energy conversion to the emission is so efficient that the wave amplitude is responsible for the brightness. We also find a polarization angle swing reflecting shock front modulation, implicating the polarization property of some repeating FRBs. The results support the shock scenario as an origin of the FRBs.