The Kabul River Basin (KRB) in Afghanistan is densely inhabited and heterogenic. The basin’s water resources are limited, and climate change is anticipated to worsen this problem. Unfortunately, there is a scarcity of data to measure the impacts of climate change on the KRB’s current water resources. The objective of the current study is to introduce a methodology that couples remote sensing and the Soil and Water Assessment Tool (SWAT) for simulating the impact of climate change on the existing water resources of the KRB. Most of the biophysical parameters required for the SWAT model were derived from remote sensing-based algorithms. The SUFI-2 technique was used for calibrating and validating the SWAT model with streamflow data. The stream-gauge stations for monitoring the streamflow are not only sparse, but the streamflow data are also scarce and limited. Therefore, we selected only the stations that are properly being monitored. During the calibration period, the coefficient of determination (R2) and Nash–Sutcliffe Efficiency (NSE) were 0.75–0.86 and 0.62–0.81, respectively. During the validation period (2011–2013), the NSE and R2 values were 0.52–0.73 and 0.65–0.86, respectively. The validated SWAT model was then used to evaluate the potential impacts of climate change on streamflow. Regional Climate Model (RegCM4-4) was used to extract the data for the climate change scenarios (RCP 4.5 and 8.5) from the CORDEX domain. The results show that streamflow in most tributaries of the KRB would decrease by a maximum of 5% and 8.5% under the RCP 4.5 and 8.5 scenarios, respectively. However, streamflow for the Nawabad tributary would increase by 2.4% and 3.3% under the RCP 4.5 and 8.5 scenarios, respectively. To mitigate the impact of climate change on reduced/increased surface water availability, the SWAT model, when combined with remote sensing data, can be an effective tool to support the sustainable management and strategic planning of water resources. Furthermore, the methodological approach used in this study can be applied in any of the data-scarce regions around the world.