Glaciers in the high mountains of Asia (HMA) make a substantial contribution to the water supply of millions of people(1,2), and they are retreating and losing mass as a result of anthropogenic climate change3 at similar rates to those seen elsewhere(4,5). In the Paris Agreement of 2015, 195 nations agreed on the aspiration to limit the level of global temperature rise to 1.5 degrees Celsius (degrees C) above pre-industrial levels. However, it is not known what an increase of 1.5 degrees C would mean for the glaciers in HMA. Here we show that a global temperature rise of 1.5 degrees C will lead to a warming of 2.1 +/- 0.1 degrees C in HMA, and that 64 +/- 7 per cent of the present-day ice mass stored in the HMA glaciers will remain by the end of the century. The 1.5 degrees C goal is extremely ambitious and is projected by only a small number of climate models of the conservative IPCC's Representative Concentration Pathway (RCP)2.6 ensemble. Projections for RCP4.5, RCP6.0 and RCP8.5 reveal that much of the glacier ice is likely to disappear, with projected mass losses of 49 +/- 7 per cent, 51 +/- 6 per cent and 64 +/- 5 per cent, respectively, by the end of the century; these projections have potentially serious consequences for regional water management and mountain communities.