This study aims to assess, in a probabilistic manner, the effect of seismic excitation direction on the performance of a 638 m‐long, 12 span prestressed concrete bridge with significant curvature in plan on the basis of overall monetary repair loss. By means of a large number of nonlinear dynamic analyses, the optimum intensity measure (IM) was selected from a pool of twenty candidates considering the impact of seismic excitation direction. Next, the variability of bridge loss with respect to the seismic incidence angle under different groups of earthquake intensities was obtained. Finally, the applicability of combination rules for the seismic performance of curved bridges was evaluated based on the multidirectional loss assessment results. Meanwhile, the effects of seismic excitation direction and earthquake intensity on the evaluation of combination rules were also revealed. Results indicate that velocity‐related or/and structural‐dependent IMs are more appropriate for the probabilistic seismic demand analysis of curved bridges. It is also notable that the total bridge loss gradually turns out to be independent of the seismic excitation direction as the seismic intensity increases and the damage develops throughout the structure. Additionally, the widely used 100/30 and 100/40 rules may lead to an unconservative estimation for the loss of the curved bridge. The above findings highlight the necessity of addressing the issue of ground motion directionality in a rigorous probabilistic manner and pave the way for further research on qualifying the influences of geometric configuration, material parameters, soil type and the consequent soil‐structure interaction effect.