Natural disasters are unavoidable and can cause serious damage to bridges, which may lead to catastrophic losses both human and economic. In the US more than 45% of bridge collapses are caused by flood events in which more than one-third are caused by scouring effects. In 2015, part of the Tadcaster bridge, a masonry arch bridge in North Yorkshire UK, collapsed during a flooding event. This tragedy was followed by another one in 2019 when a masonry bridge collapsed in the same county. Therefore, the assessment of bridges susceptible to these events is of paramount importance as to identify possible mitigation needs. The objective of the present paper is to present a consistent framework to obtain the reliability index of a masonry arch bridge (MAB), under flood hazard that is subject to local scour, using surrogate models to reduce the computational effort of the probabilistic analysis. The proposed framework is tested on a MAB located in Portugal. A two-dimensional numerical model is constructed where the random variables that affect the structural capacity and the scour geometry were considered. The results show the failure mechanism of the MAB when subjected to scour-induced settlements, therefore allowing to identify the vulnerable zones along the arch's length. The presented methodology can be used to assess the bridge performance under a flood event, thus providing useful information for bridge management and monitoring. Moreover, it can be further developed to include fragility analysis and vulnerability assessment.