The Jinsha River basin (JRB), known as China’s largest hydropower base, has been facing a surge in hydrological drought occurrences in the past several years. This study used the drought index model and soil and water assessment tool (SWAT) hydrological model to uncover the linkages between meteorological and hydrological drought using long-term datasets in the JRB. The results revealed that: (1) Over the past six decades, the JRB has experienced recurrent meteorological droughts, with the upper reaches being the most affected, accounting for a frequency of 17.5%. However, the frequency of drought in the middle and lower reaches has shown a marked increase in the last 15 years. (2) The frequency of hydrological drought in the JRB has been on the rise over the past six decades, with a particularly notable increase observed in the last two decades. Furthermore, a noticeable upward trend has been observed in the duration of these hydrological droughts. (3) The propagation durations from meteorological drought to hydrological drought exhibited noticeable seasonal differences in the JRB. The transmission duration during the flood season was shorter, whereas in the dry season, it was more protracted. Additionally, the connection between meteorological drought and hydrological drought demonstrates a weakening trend. The findings of this study hold significant implications for crafting an efficient reservoir dispatching strategy to safeguard the water security of the JRB.