A number of recent flash floods and debris flows, which were triggered by glacier avalanches from relatively small but steep hanging glaciers have exposed the vulnerability of infrastructures and livelihoods in the high Himalaya. As of now, there are no methods to identify potentially dangerous hanging glaciers in a catchment, and to assess the associated risk to any infrastructure. In this study, we propose a simple physics-based, probabilistic method to provide a first-order solution to this problem. It is based on considering a large number of hypothetical glacier avalanches and associated flood events within a numerically-efficient Monte-Carlo framework. We assign probability weights to the chain of events involved in any flood reaching a given dam location. To assess the relative risk, we test the method in three Himalayan catchments, including two where glacier avalanche events have been reported in the recent past. The proposed method is based on a series of simplifying assumptions regarding the initiation and propagation of the events, necessitated by the complexity of the processes involved and a lack of data in these remote environments. Our method performs reasonably well in two of the studied Himalayan catchments, while limitations in the performance of the method are apparent in one of the studied catchments. A better understanding of the underlying processes may help with more accurate parameterisations of the weights assigned to the chain of events. The presented method may be considered a starting point to quantify the risk posed by increasingly unstable ice on high and steep slopes to hydropower infrastructures in the Himalayan catchments.