Due to climate change, the frequency and duration of meteorological drought have increased. In addition, local water supply capacity has not met water demand in many regions, which will eventually lead to serious water shortages. To mitigate the effects of drought on sustainable water use, it is necessary to understand how climate change affects regional water supply capacity and drought risk. To this end, this study evaluated the drought response capacity of regional water supply systems and assessed the comprehensive drought risk in terms of drought hazard, vulnerability, and response capacity. To avoid subjectivity in risk analysis, structural equation modeling was used to select primary indicators and probability and statistical methods were used to assign weights to the indicators. The changes in drought risk in different climate change scenarios were assessed using sensitivity analyses. The overall results indicate that the future drought risks in Gyeonggi, Gyeongsang, Chungcheong, Jeolla, and Gangwon are 18, 12, 13, 9, and 10% higher, respectively, than the current risk level. The sensitivity analyses showed that Jinju in Gyeongsang province, which has a high drought response capacity, had the largest decreasing rate in drought risk. The quantified changes in drought risk under future climate change scenarios will be useful for identifying areas with a high drought risk and making decisions about drought mitigation under climate change.