Interface debonding between fiber reinforced polymers (FPR) and substrates is the principal failure mode for FRP-reinforced structure. To understand the bond–slip relationship at FRP-to-brick interfaces under dynamic loading, the influences of the dynamic enhancement of material performance on the bond–slip curve were studied. Single-lap shear tests under two different loading rates were performed, and the slip distribution curves at different loading stages were fitted to derive the bond–slip relationship. Then a numerical model considering the strain rate effects on materials was built and verified with test results. Further, the influences of brick strength, FRP stiffness and slip rate on the bond–slip relationship were investigated numerically. The research results show that FRP stiffness mainly influences the shape of the bond–slip curve, while brick strength mainly influences the amplitude of the bond–slip curve. The variations of the bond–slip relationship under dynamic loading, i.e., under different slip rates, are mainly caused by the dynamic enhancement of brick strength, and also by the dynamic enhancement of FRP stiffness, especially within a specific slip rate range. The proposed empirical formula considering dynamic FRP stiffness and dynamic brick strength can be used to predict the bond–slip relationship at the FRP-to-brick interface under dynamic loading.