Climate change directly impacts the hydrological cycle via increasing temperatures and seasonal precipitation shifts, which are variable at local scales. The water resources of the Upper Yangtze River Basin (UYRB) account for almost 40% and 15% of all water resources used in the Yangtze Basin and China, respectively. Future climate change and the possible responses of surface runoff in this region are urgent issues for China’s water security and sustainable socioeconomic development. This study evaluated the potential impacts of future climate change on the hydrological regimes (high flow (Q5), low flow (Q95), and mean annual runoff (MAR)) of the UYRB using global climate models (GCMs) and a variable infiltration capacity (VIC) model. We used the eight bias-corrected GCM outputs from Phase 5 of the Coupled Model Intercomparison Project (CMIP5) to examine the effects of climate change under two future representative concentration pathways (RCP4.5 and RCP8.5). The direct variance method was adopted to analyze the contributions of precipitation and temperature to future Q5, Q95, and MAR. The results showed that the equidistant cumulative distribution function (EDCDF) can considerably reduce biases in the temperature and precipitation fields of CMIP5 models and that the EDCDF captured the extreme values and spatial pattern of the climate fields. Relative to the baseline period (1961–1990), precipitation is projected to slightly increase in the future, while temperature is projected to considerably increase. Furthermore, Q5, Q95, and MAR are projected to decrease. The projected decreases in the median value of Q95 were 21.08% to 24.88% and 16.05% to 26.70% under RCP4.5 and RCP8.5, respectively; these decreases were larger than those of MAR and Q5. Temperature increases accounted for more than 99% of the projected changes, whereas precipitation had limited projected effects on Q95 and MAR. These results indicate the drought risk over the UYRB will increase considerably in the future.