Although only a few of the ancient masonry arch bridges (MABs) are in fairly good condition today, many ancient arch bridges are still in use. Over time, the condition of the masonry bridges declines and the safety requirements change. Therefore, it is important to examine these bridges under different influences. The strengthening of MABs is generally not essential. The major cause of damage to MABs is their insufficient width and height, and thus, it is not the safety but the usability that has restricted the life-time of the MABs. Therefore, in this investigation, the effect of the arch height on the static and dynamic behavior of a single-span MAB was investigated. For this aim, the Ancient Tokatlı Bridge, built in Karabük, Türkiye, was selected for investigation under near-fault (NF) and far-fault (FF) ground motions (GMs). To observe the altitude of the arch warp on the ancient MAB, first, the finite element model (FEM) was utilized, using ANSYS and SAP 2000. Furthermore, to constitute the arch warp’s influence on a MAB, the FEM was remodeled considering the different arch warps between 7.0 and 9.0 m. Moreover, GMs were applied to the FEM to investigate the effect of dynamic behavior. Under these GMs, stresses and strains (compression and tensile) were observed and compared with each other. Consequently, at the end of these investigations, it was observed that the maximum motions were reduced, while the height of the one-span MAB was increased under NF and FF GMs, and this was also true for the contrary situations. The compression stresses were not observed to be hazardous at the point of destruction, while the altitude of the one-span MAB increased.