This study aims to estimate the surface runoff and examine the impact of climate change on water resources in the Upper Kabul River Basin (UKRB). A hydrological model was developed using the Soil and Water Assessment Tool (SWAT) from 2009 to 2019. The monthly calibration was conducted on streamflow in six stations for the period from 2010 to 2016, and the results were validated from 2017 to 2018 based on available observed data. The hydrological sensitivity parameters were further prioritized using SWAT-CUP. The uncertainty of the model was analyzed by the 95% Prediction Uncertainty (95PPU). Future projections were analyzed for the 2040s (2030–2049) and 2090s (2080–2099) compared to the baseline period (1986–2005) under two representation concentration pathways (RCP4.5, RCP8.5). Four Regional Climate Models (RCMs) were bias-corrected using the linear scaling bias correction method. The modeling results exhibited a very reasonable fit between the estimated and observed runoff in different stations, with NS values ranging from 0.54 to 0.91 in the calibration period. The future mean annual surface runoff exhibited an increase in the 2040s and 2090s compared to the baseline under both RCPs of 4.5 and 8.5 due to an increase in annual precipitation. The annual precipitation is projected to increase by 5% in the 2040s, 1% in the 2090s under RCP4.5, and by 9% in the 2040s and 2% in the 2090s under RCP8.5. The future temperature is also projected to increase and consequently lead to earlier snowmelt, resulting in a shift in the seasonal runoff peak to earlier months in the UKRB. However, the shifts in the timing of runoff could lead to significant impacts on water availability and exacerbate the water stress in this region, decreasing in summer runoff and increasing in the winter and spring runoffs. The future annual evapotranspiration is projected to increase under both scenarios; however, decreases in annual snowfall, snowmelt, sublimation, and groundwater recharge are predicted in the UKRB.