The progressive damage behaviors of woven fabric-reinforced natural rubber panels under low-velocity impact were studied by the drop-weight tests. The woven fabrics considered include nylon, Kevlar, and carbon. The impact force, impact energy, and delamination area were analyzed, and the damaged samples were observed using an optical microscopy and an X-ray scanner to investigate the damage mechanisms. The results show that the peak force of impact increases while the absorbed energy decreases as the fiber strength/stiffness and fiber content increase. Based on the peak force and the delamination area results, the natural rubber/Carbon/2 specimen, which consists of two carbon fabric layers inside the natural rubber, displays the best impact performance among the composites considered in this study.