The Himalayan River basins, essential for water, food, and energy security in Asia, are undergoing rapid hydroclimatic change. This study provides a quantitative assessment of these impacts on the Babai River Basin (BRB) in Nepal through the integration of historical hydrological data (1990–2020) with future climate projections from the ACCESS-CM2 model under the SSP2–4.5 scenario. A Quantile Delta Mapping (QDM) bias correction was applied to the climate data. A Monsoon-Optimized Distributed Lag Model (MODLM) was developed and rigorously validated (Nash-Sutcliffe Efficiency >0.75), demonstrating high efficacy in simulating the basin’s dominant monsoon-driven discharge regime. Results project a significant temperature increase of approximately 4 °C by 2100, which, despite a modest rise in total precipitation, intensifies evapotranspiration and exacerbates water stress, particularly during the critical pre-monsoon period. Uncertainty analysis confirms that future water availability is highly sensitive to emission pathways. The subsequent vulnerability assessment identifies irrigation water security and groundwater-dependent springs as the most critical climate risks. This research concludes that proactive adaptation, centered on integrated water resources management, climate-resilient agriculture, and community-based storage, is imperative to ensure the water security and socio-ecological resilience of the BRB under a changing climate.