In recent years, the Mediterranean basin has been characterized as a climate change hotspot due to its rapid transition to warmer conditions and the strong agreement among most climate models predicting a significant decrease in precipitation by the end of the 21st century. These robust signals of climate change highlight the region’s high susceptibility to hydrometeorological extremes, such as droughts, which are expected to become more frequent, prolonged, and intense. In this context, the present study focuses on Greece, a country vulnerable to drought events, where the increasing risk of water scarcity threatens critical sectors such as food security, energy production, public health, and ecosystem resilience. To assess future drought conditions in the country, the Standardized Precipitation Index (SPI) was selected due to its statistical robustness and widespread adoption as a key drought monitoring tool. The SPI was calculated at a 12-month timescale for 58 meteorological stations across Greece, focusing on the late 21st century (2071–2100). The required precipitation data were extracted from high-resolution regional climate simulations under two Representative Concentration Pathways: the intermediate stabilization scenario (RCP4.5) and the high-emission scenario (RCP8.5). The climate model’s performance was evaluated using statistical metrics—RMSE, MAE, MSE, and WAPE—and by comparing the frequency distributions of observed and simulated precipitation for the reference period (1971–2000). To identify spatially homogeneous regions in terms of future drought variability, Principal Component Analysis (PCA) was applied to the SPI dataset under RCP8.5, targeting areas with the highest drought susceptibility. Drought characteristics—severity (S) and duration (D)—were further analyzed at representative stations from these PCA-derived regions using Run Theory, enabling a comparative evaluation between RCP4.5 and RCP8.5. The results reveal more prolonged and severe droughts by the late 21st century, particularly in eastern Crete and southeastern Peloponnese, emphasizing the urgent need for targeted adaptation measures in these highly vulnerable regions.