The Nepalese Sunsari Morang Irrigation district is the lifeblood of millions of people in the Koshi River basin. Despite its fundamental importance to food security, little is known about the impacts of climate change on future irrigation demand and grain yields in this region. Here, we examined the impacts of climate change on the irrigation demand and grain yield of wheat crop. Climate change was simulated using Representative Concentration Pathways (RCPs) of 4.5 and 8.5 for three time horizons (2016–2045, 2036–2065, and 2071–2100) in the Agricultural Production Systems Simulator (APSIM). For the field data’s measured period (2018–2020), we showed that farmers applied only 25% of the irrigation water required to achieve the maximum potential grain yield. Actual yields were less than 50% of the potential yields. Projected irrigation water demand is likely to increase for RCP4.5 (3%) but likely to decrease under RCP8.5 (8%) due to the truncated crop duration and lower maturity biomass by the end of the 21st century. However, simulated yields declined by 20%, suggesting that even irrigation will not be enough to mitigate the severe and detrimental effects of climate change on crop production. While our results herald positive implications for irrigation demand in the region, the implications for regional food security may be dire.