The London-based Free Tibet says 52-year-old Tamdrin Dorjee died at the scene Saturday near Tso Monastery in northwestern China's Gansu province.
It says the man is the grandfather of the 7th Gungthang Rinpoche, believed by Tibetan Buddhists to be the reincarnation of an important religious figure.
It says Dorjee's body was taken to his home village. Photos said to be from the scene show dozens of villagers and monks gathered around a body in smoke.
Free Tibet says more than 50 Tibetans have self-immolated to protest China's rule of the Himalayan region.