Himalayan water resources attract a rapidly growing number of hydroelectric power projects (HPP) to satisfy Asia's soaring energy demands. Yet HPP operating or planned in steep, glacier-fed mountain rivers face hazards of glacial lake outburst floods (GLOFs) that can damage hydropower infrastructure, alter water and sediment yields, and compromise livelihoods downstream. Detailed appraisals of such GLOF hazards are limited to case studies, however, and a more comprehensive, systematic analysis remains elusive. To this end we estimate the regional exposure of 257 Himalayan HPP to GLOFs, using a flood-wave propagation model fed by Monte Carlo-derived outburst volumes of >2300 glacial lakes. We interpret the spread of thus modeled peak discharges as a predictive uncertainty that arises mainly from outburst volumes and dam-breach rates that are difficult to assess before dams fail. With 66% of sampled HPP are on potential GLOF tracks, up to one third of these HPP could experience GLOF discharges well above local design floods, as hydropower development continues to seek higher sites closer to glacial lakes. We compute that this systematic push of HPP into headwaters effectively doubles the uncertainty about GLOF peak discharge in these locations. Peak discharges farther downstream, in contrast, are easier to predict because GLOF waves attenuate rapidly. Considering this systematic pattern of regional GLOF exposure might aid the site selection of future Himalayan HPP. Our method can augment, and help to regularly update, current hazard assessments, given that global warming is likely changing the number and size of Himalayan meltwater lakes.