Narok County in Kenya is the home to the Maasai Mara Game Reserve, which offers important habitats for a great variety of wild animals, hence, a hub for tourist attraction, earning the county and country an extra income through revenue collection. The Mau Forest Complex in the north is a source of major rivers including the Mara River and a water catchment tower that supports other regions as well. Many rivers present in the region support several activities and livelihood to the people in the area. The study examined how the quantity of surface water resources varied under the different climate change scenarios, and the sensitivity of the region to a changing climate. Several datasets used in this study were collated from different sources and included hydro–meteorological data, Digital Elevation Model (DEM), and Coordinated Regional Downscaling Experiment (CORDEX) climate projections. The WEAP (Water Evaluation and Planning) model was applied using the rainfall–runoff (soil moisture method) approach to compute runoff generated with climate data as input. All the calculations were done on a monthly time step from the current year account to the last year of the scenario. Calibration of the model proceeded using the PEST tool within the WEAP interface. The goodness of fit was evaluated using the coefficient of determination (R2), percentage bias (PBIAS), and Nash–Sutcliffe efficiency (NSE) criterion. From the tests, it was clear that WEAP performed well in simulating stream flows. The coefficient of determination (R2) was greater than the threshold R2 > 0.5 in both periods, i.e., 0.83 and 0.97 for calibration and validation periods, respectively, for the monthly flows. A 25-year mean monthly average was chosen with two time slices (2006–2030 and 2031–2055), which were compared against the baseline (1981–2000). There will be a general decrease in water quantity in the region in both scenarios: −30% by 2030 and −23.45% by 2055. In comparison, RCP4.5 and Scenario3 (+2.5°C, +10% P) were higher than RCP8.5 and Scenario 2 respectively. There was also a clear indication that the region was highly sensitive to a perturbation in climate from the synthetic scenarios. A change in either rainfall or temperature (or both) could lead to an impact on the amount of surface water yields.