As the span of concrete-filled steel tube (CFST) arch bridges increases, the hydration heat temperature effect of concrete inside steel tube becomes more severe, which increases the safety risk during the construction process. Therefore, a numerical simulation of the mechanical response of a long-span CFST arch bridge under the influence of hydration heat was carried out. First, based on the hydration heat conduction theory, a finite element model of the transient temperature field of a CFST arch rib was established. The temperature distribution of the CFST arch rib and its variation with time were revealed, and an approximate formula for the distribution of the hydration heat temperature along the radial direction of the CFST was provided. Subsequently, the variation law of the thermal stress of a CFST during hydration heat release was investigated. Finally, based on the principle of temperature equivalence, a finite element model of the overall CFST arch rib was established to examine the effect of hydration heat on the deformation of the arch rib. The results reveal that the hydration heat temperature field of the CFST arch rib exhibits nonlinear and axisymmetric characteristics. The maximum temperature of the section and the maximum temperature difference can reach 73.5 °C and 33.2 °C, respectively. Because of the influence of the hydration heat, there is a significant stress gradient in the cross section of the arch rib. A maximum radial stress of 2.08 MPa is attained, indicating a risk of concrete cracking. Additionally, the displacement along the transverse and vertical directions of the chord tube exhibits an initial increase, followed by a decrease over time. The maximum transverse displacement of the chord tube reaches 70.6 mm, while the vertical displacement reaches 117.8 mm.