Drought risk assessment based on a reliable, integrated index that encompasses meteorological, hydrological, and agricultural dimensions is critical for understanding future drought trends and for implementing effective prevention and mitigation strategies. This study aims to develop a Multivariate Integrated Drought Index (MIDI) by combining four key drought indicators—Streamflow Drought Index (SDI), Standardized Runoff Index (SRI), Standardized Precipitation Index (SPI), and Standardized Precipitation-Evapotranspiration Index (SPEI)—to enable a holistic evaluation of drought risk. The study area, the Sarbaz River Basin in southeastern Iran, is the region’s only permanent river system and holds strategic importance for agricultural development and unique ecological sustainability, particularly under escalating water scarcity driven by climate change and population growth. The MIDI was constructed using variable fuzzy set theory and the entropy weight method. Drought events were subsequently redefined by duration and severity based on run theory. Copula functions were employed to model the joint distribution of drought duration and severity for comprehensive assessment of drought risk. Results indicate that the MIDI is well correlated with the individual meteorological and hydrological drought indices and demonstrates greater sensitivity and efficiency in capturing historical drought events compared to single indices. The Sarbaz River Basin has experienced over 100 drought events, with an average inter-event interval of five months. Droughts of varying severity occur annually. Given this high frequency, water resource management should incorporate the MIDI outputs and the joint duration–severity analysis to formulate proactive adaptation strategies. Future research should investigate climatic and land-use impacts on drought dynamics within this critical basin.