Kabul River Basin is one of the most significant river basins in Afghanistan from a socio-economic perspective. Since the country is located in an arid climate zone with drastically varying climatic behavior, an effective assessment of meteorological drought is very essential to managing the limited availability of water resources. For this endeavor, the outputs of three general circulation models under two representative concentration pathways (RCP 4.5 and RCP 8.5) were used against the baseline period of 1961–1980. Different bias correction methods were applied, and the results show that the delta change method, quantile mapping method, and empirical quantile mapping all performed better for the precipitation, maximum temperature, and minimum temperature datasets, respectively. The ERA5-Land datasets and WorldClim Version 2 are used to validate the bias-corrected precipitation and temperature datasets, respectively, to determine their dependability, and the results were found to be promising. Standardized Precipitation Index (SPI), Reconnaissance Drought Index (RDI), Deciles Index (DI), and New Drought Index (NDI) were used to assess the drought condition in the past and forecast for the future periods of the 2020s, 2050s, and 2080s. The spatial distribution of assessed drought indices was mapped using the inverse distance weighting (IDW) method. Our results revealed that moderate to extreme droughts are consistent across the entire basin. This might be because the projected annual precipitation in the river basin shows a decline of 53–65% up to the end of this century (2100), and the average annual temperature is projected to increase by 1.8 °C, 3.5 °C, and 4.8 °C, respectively, for the three future periods of the 2020s, 2050s, and 2080s. Furthermore, the results show that the drought estimated by SPI and RDI for future climate scenarios is almost the same, whereas NDI estimates frequent drought events after the 2050s. However, for moderate drought, RDI, which includes the effects of evapotranspiration, was found to be far greater than SPI under both scenarios, and NDI considering temperature and precipitation also estimates a larger number of drought years, strengthening the possibility of its occurrence in the basin. A regional comparison of drought also indicates a decrease in precipitation in future periods, predominantly in high altitudes.