Europe’s historic masonry arch bridges are culturally and economically significant, but their long-term safety must be ensured. Scour effects are the most common cause of collapse, so it is necessary to carry out structural assessments to mitigate the risk and prevent potential failures. In this study, a metamodel-based method was used to determine the probability of failure of an existing stone arch bridge in Portugal due to local and contraction scour on the abutments. Non-linear finite element analysis supported the calculation of the reliability index, which took into account the soil-structure interaction and the failure mechanism. The variables with the greatest influence on the load-carrying capacity of the structure were identified and a surrogate model was implemented. Fragility curves were then derived based on the surrogate model, using scour depth as a measure of intensity and load factor as an engineering requirement parameter. The results of the study indicate that the load capacity of the numerical model is compromised when the scour depth of 1.5 m reaches the base of the foundation. As a result, stability problems and settlements are observed in the model. At a depth of 2.5 m, the soil reaches its ultimate bearing capacity.