The Lower Mekong River is one of the significant rivers nurturing people on the Southeast Asian mainland. Its tributaries include the Mun River (NE Thailand), which often experiences extreme water events. In this study, the streamflow change in the year 2115 was simulated by relying on the Half-a-Degree Additional Warming, Prognosis and Projected Impacts (HAPPI) experiment and the Model for Interdisciplinary Research on Climate, version 5 (MIROC5) climate model for average global warming of 1.5 °C (Plus1.5) and 2.0 °C (Plus2.0) above pre-industrial levels and compared with the base year in 2015 for the Mun River Basin. The Soil–Water Assessment Tool (SWAT) was used for the streamflow simulation. The results showed an increasing air temperature against lowering rainfall and relative humidity (except for the post-monsoon months), suggesting overall rain suppression in response to the warming climate. The median projected annual streamflow to the Mekong River in 2115 decreased for both ‘Plus1.5’ (−32.5%, median) and ‘Plus2.0’ (−23.1%, median). However, increasing annual streamflow could be found only in the middle part. Seasonal streamflow changes revealed a different spatiotemporal response to climate change resulting in inconsistent streamflow changes across the basin. The adaptive measures for the middle part should be focused on flooding control, whereas the upper and the lower parts should be against drought.