Glaciers around the world are shrinking rapidly and will continue to do so in the next decades. Anticipating the consequences resulting from such glacier changes is key to design and implement adequate mitigation measures. Here, we focus on the future evolution of potential ice-dammed and supraglacial lakes in High Mountain Asia, as such lakes are responsible for the majority of glacier lake outburst floods in the region. We identify 11,129 potential lakes at present, with a total maximum volume of 2070 million m³. We find a strong correlation between large modelled lakes and historical outburst floods. By accounting for the evolution of glaciers under different climate change mitigation measures, we project that the number of potential ice-dammed lakes could increase by between 15 and 18% until 2080, with a concomitant 45–55% increase in their volume. Our findings thus suggest that a temporary increase of glacier lake outburst floods is to be expected in the coming decades.