Hydrological models serve as valuable instruments for assessing the impact of climate change on water resources and agriculture as well as for developing adaptation measures. In Yemen, climate change and variability are imposing a significant impact on the most important sectors such as agriculture and economy. The current study evaluates the influence of future climate on hydrology and water balance components in Yemen’s highlands using a semi-distributed physical-based hydrologic model Soil Water Assessment Tool (SWAT) and employing high-resolution climate projections. The SWAT was calibrated and verified using observed streamflow data from 1982 to 2000 in three large catchments. Ground data from 24 stations and statistically downscaled future climate data for the period 2010–2100 under RCP2.6 and RCP8.5 are used. SWAT performance was assessed using multiple statistical methods, which revealed the commendable performance of SWAT during the calibration (average NSE = 0.80) and validation (NSE = 0.72) periods. The outcome indicates an increase in future seasonal and annual rainfall, maximum temperature, and minimum temperature in the 2020s and the 2080s under both RCP2.6 and RCP8.5 scenarios. This projected increase in the rainfall and the local temperature will result in increased averages of surface runoff, evapotranspiration, soil water, and groundwater recharge in the representative three catchments up to 6.5%, 21.1%, 7.6%, and 6.4%, respectively. Although, the projected increase in the water balance components will benefit the agriculture and water sector, specific adaptation measures will be crucial to mitigate potential flood impacts arising from the increased precipitations as well as to minimize the consequences of the increased temperature. Likewise, demand for supplementary irrigation is expected to increase to offset the higher evapotranspiration rates in the future.