To investigate the most unfavorable fire case and the mechanical behavior of the arch ribs in a swallow-type arch bridge, fire cases were simulated in this study based on a gasoline tanker heat release rate of 300 MW, comprehensively considering wind speeds and different fire locations (across different lanes in the transverse direction at the intersection of the arch rib and the bridge deck). The Fire Dynamics Simulator (FDS) method was utilized to obtain the fire temperature field of the arch rib, and a thermal analysis model was established to analyze the temperature fields of the steel box arch rib under different cases, thereby determining the most unfavorable fire case. Furthermore, a thermo-structural coupled analysis model was established using ANSYS software to study the mechanical behavior of the steel box arch rib under the most unfavorable fire case. It is indicated by the results that the greatest impact on the arch rib is caused by the fire case with higher wind speeds and a fire location closer to the arch rib (i.e., case W8-LA). Under this most unfavorable case, significant non-uniform temperature rise characteristics are exhibited by the cross-section of the arch rib, and a peak temperature of up to 890°C is reached under a quasi-steady state, which far exceeds the critical temperature of 550°C for steel. Affected by the thermo-mechanical coupling effect, the yield state of the component is reached at 460 s after ignition; a peak stress of 387.2 MPa is reached at 500 s, which is followed by stress unloading due to the high-temperature softening and significant stiffness degradation of the material. At this stage, a highly localized trend of plastic damage is exhibited, with the maximum displacement of the fire-exposed center cross-section reaching 37.632 mm, and the maximum plastic deformation being increased by approximately 18.4%. It is indicated by the aforementioned profound plastic deformation that the load-bearing capacity limit of the arch rib has been reached, severely threatening the overall stability of the structure.