Assessing the impact of climate change is essential for developing water resource management plans, especially in areas facing severe issues regarding ecosystem service degradation. This study assessed the effects of climate change on the hydrological balance using the SWAT (Soil and Water Assessment Tool) hydrological model in the Mixteco River Basin (MRB), Oaxaca, Mexico. Temperature and precipitation were predicted with the projections of global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6); the bias was corrected using CMhyd software, and then the best performing GCM was selected for use in the SWAT model. According to the GCM MPI-ESM1-2-LR, precipitation might decrease by between 83.71 mm and 225.83 mm, while temperature might increase by between 2.57 °C and 4.77 °C, causing a greater atmospheric evaporation demand that might modify the hydrological balance of the MRB. Water yield might decrease by 47.40% and 61.01% under the climate scenarios SP245 and SSP585, respectively. Therefore, adaptation and mitigation measures are needed to offset the adverse impact of climate change in the MRB.