Hydroclimatic process in the Yarlung Tsangpo River (YTR) basin, a sensitive area to climate change, is obviously changing during recent years, but there has limited understanding about it. In this study, we investigated the spatiotemporal variation of precipitation over last four decades in the basin and the impact thereon of the changing Indian summer monsoon at interannual and decadal time scales. All the precipitation series have similar scaling behavior, reflecting similar climatic regime throughout the basin. However, the effect of the Indian monsoon strengthens from the downstream to upstream, causing spatial variability in the seasonal distribution of precipitation, and on this basis, the YTR basin is roughly divided into three regions: east, middle, and west. Both the occurrence times and magnitude of precipitation extremes, ranging 25–50 mm/d, are exhibiting downward trends over the last four decades, which bodes well for water disaster controls in the basin. The Indian summer monsoon index, as an intensity indicator for the Indian summer monsoon, shows a positive relationship with the summer precipitation in the YTR basin. Periodic variability of the Indian monsoon determines the interannual nonstationary fluctuations of precipitation. Especially, the weakening effect of the Indian summer monsoon has caused an obvious decrease in precipitation over the rainy season after 1998. If the Indian summer monsoon keeps weakening, the precipitation would decrease and potentially water shortage would become more severe in the basin. Effective adaptation strategy should therefore be developed proactively to handle the unfavorable water situation, which is likely to occur in the future.