Under the influence of global climate change, hydrological drought events in the Yangtze River have occurred frequently with an increasing intensity, seriously threatening food security and economic development. This study uses the monthly water balance model developed by the Research Center for Climate Change (i.e., the RCCC-WBM model) to analyze the historical evolution and future trends of hydrological features in four hydrological stations (Zhimenda, Zhutuo, Cuntan, and Yichang) in the upper reaches of the Yangtze River and the basins above. Meanwhile, hydrological drought events and their characteristics are identified based on the Standardized Runoff Index (SRI). The results show that: (1) From 1961 to 2020, the runoffs of Zhutuo, Cuntan, and Yichang hydrological stations, along with the SRI of the main stream area in the upper reaches of the Yangtze River and the sub-basins of the Minjiang, Tuojiang, Jialing, and Wujiang River, exhibited a decreasing trend, indicating a slight drying trend, while the runoff of the Zhimenda hydrological station and the SRI of the Jinsha River basin above it showed an increasing trend, suggesting no drought tendency. (2) From 2021 to 2090, the SRI of each hydrological station and its upstream basins all showed an increasing trend, indicating that the upper reaches of the Yangtze River have no drought tendency in the future; this may be closely related to the significant increase in projected precipitation and runoff. The frequency, occurrence rate, duration, and intensity of hydrological droughts will be stronger in the near term and weaker in the long term. Given the increasingly prominent extreme hydrological droughts in the upper reaches of the Yangtze River, drought prevention and disaster reduction becomes urgent. It is recommended to improve the drought combating mechanism and system, strengthen infrastructure construction and emergency management capabilities, promote the digital technology to build a smart drought-prevention and disaster-reduction system, and highlight technological innovation to strengthen the scientific and technological support for drought prevention and mitigation.