Climate change has an impact on water resources. Estimations of the variations in water balance under climate change variables are essential for managing and developing the water resource of a catchment. The current investigation evaluated the magnitude of the change in the water balance component of the Akaki catchment, Ethiopia, using the semi-distributed hydrological model, the Soil and Water Assessment Tool (SWAT), with the integration of the Coordinated Regional Downscaling Experiment of Africa under RCP4.5 and 8.5. The SWAT model was developed using spatial and temporal data; it was calibrated (1991–2001) and validated (2002–2004) using SWAT-CUP. The statistical monthly SWAT model performance values of the NSE, PBIAS (%), and R2 showed good agreement between calibration and validation. On an annual basis, projected rainfall is expected to increase by 14.96%, 4.13%, 8.39%, and 10.39% in the 2040s under RCP4.5 and 8.5 and in the 2060s under RCP4.5 and 8.5, respectively, with inconsistent change on a monthly projections basis for each scenario. The projected monthly and yearly temperatures are expected to increase under different climate change scenarios. Annual evapotranspiration and potential evapotranspiration increased under both RCPs, whereas surface runoff, lateral flow, and water yield declined under the climate scenarios of each RCP. Monthly projected water yield showed a non-uniform change in the first 30 years and in the second years under the RCP4.5 and RCP8.5 scenarios. These results show that the catchment is highly vulnerable to hydrological and agricultural drought due to water availability. These research findings provide valuable evidence on the role of climate change in water balance, which will help decision makers to achieve better water resource management.