The security assessment of high arch dams is a significant topic that has been researched in recent years. It is troublesome to develop a security assessment for high arch dams under far-field underwater blasts because the high arch dam is a sophisticated statically indeterminate spatial shell structure, and the underwater blasting shock wave has the characteristics of a large peak value and high frequency. Hence, the fragility analysis of a 300-m-high arch dam against a far-field underwater blast based on the probabilistic method is conducted for safety evaluation with the index of downstream peak displacement (and Downstream Peak Displacement-Span ratio). The fragility analysis process of the high arch dam under the far-field underwater blast is proposed for the first time. The impact of foundation plasticity on the high arch dam under far-field underwater blast is discussed regarding dynamic response and damage patterns with the coupled acoustic-structural (CAS) method first. The damage limit states are presented based on different damage patterns and index values from enormous computational schemes. The fragility curves with different indexes of downstream peak displacement, upstream peak displacement, and damage volume ratio are also compared. The fragility curves of the high arch dam against the far-field underwater blast with different explosive distances of 50 to 200 m are established with the Artificial Neural Network method. The results demonstrate that the non-linear dynamic response and damage of the high arch dam under the far-field underwater blast are significantly influenced by the foundation plasticity, especially for vibration upstream and damage of the foundation face. The explosive situations with an explosive distance of 50–100 m and explosive weight of more than 12000 kg cause a greater threat to the security of the high arch dam with the probability of severe damage approaching 100 %. The explosive situations with an explosive distance of more than 150 m or explosive weight of less than 3000 kg have a small effect. The research results can be used as a reference when conducting safety assessments of high arch dams to blasting loads.