Irrigated agriculture in South Asia depends on meltwater, monsoon rains and groundwater. Climate change alters the hydrology and causes shifts in the timing, composition and magnitude of these sources of water supply. Simultaneously, socio-economic growth increases water demand. Here we use a high-resolution cryosphere–hydrology–crop model forced with an ensemble of climate and socio-economic projections to assess how the sources of irrigation water supply may shift during the twenty-first century. We find increases in the importance of meltwater and groundwater for irrigated agriculture. An earlier melt peak increases meltwater withdrawal at the onset of the cropping season in May and June in the Indus, whereas increasing peak irrigation water demand during July and August aggravates non-renewable groundwater pumping in the Indus and Ganges despite runoff increases. Increasing inter-annual variability in rainfall-runoff increases the need for meltwater and groundwater to complement rainfall runoff during future dry years.