A Tibetan monk set himself on fire and died on Sunday in the far western province of Qinghai, suggesting that a wave of self-immolations among Tibetans that poses a major challenge for both Beijing and exiled Tibetan leaders could be spreading.

The man died after lighting himself on fire early Sunday morning in downtown Gyumai, in the Golog Tibetan Autonomous Prefecture, the state-run Xinhua news agency reported. The monk was a living Buddha, the reports said, meaning he was a senior spiritual leader in Tibetan Buddhism. The...