Seismic analysis of historical masonry bridges is important for authorities in all countries hosting such cultural heritage assets. The masonry arch bridge investigated in this study was built during the Roman period and is on the island of Rhodes, in Greece. Fifteen seismic records were considered and categorized as far-field, pulse-like near-field, and non-pulse-like near-field. The earthquake excitations were scaled to a target spectrum, and nonlinear time-history analyses were performed in the transverse direction. The performance levels were introduced based on the pushover curve, and the post-earthquake damage state of the bridge was examined. According to the results, pulse-like near-field events are more damaging than non-pulse-like near-field ground motions. Additionally the bridge is more vulnerable to far-field excitations than near-field events. Furthermore, the structure will suffer extensive post-earthquake damage and must be retrofitted.