The incident is the latest of dozens of self-immolations by Tibetans since 2009.
Free Tibet said 52-year-old Tamdrin Dorjee died at the scene near Tsoe Monastery in northwestern China's Gansu province.
It said the man is the grandfather of the 7th Gungthang Rinpoche, believed by Tibetan Buddhists to be the reincarnation of an important religious figure.
Dorjee's body was taken to his home village, Free Tibet said. Photos said to be from the scene show dozens of villagers and monks gathered around a body in smoke.
The self-proclaimed Tibetan government-in-exile confirmed the report. It said a heavy presence of paramilitary police in and around the monastery followed the self-immolation.
More than 50 Tibetans have self-immolated to protest China's rule of the Himalayan region, and most of them have died, according to tallies by Tibetan rights groups.
The government-in-exile has urged Tibetans not to give up their lives in self-immolation protests. Meanwhile, it tries to gain international support for their struggles against China's rule.
Calls to the government and police offices for Gannan Tibetan Autonomous Prefecture, where the self-immolation took place, rang unanswered Saturday evening.
China has blamed the Tibetans' exiled spiritual leader, the Dalai Lama, for inciting the immolations, but he denies the claim.
More Nation & World Headlines
ISIS destroys ancient Phoenician temple at Palmyra 4:39 p.m. Help save the planet, skip the salad 6:38 p.m. Studies show chemical risk to coffee roasters, grinders California drought may exacerbate wildlife-human encounters Casey Anthony prosecutor used adultery website Planes collide at Swiss airshow, killing 1 pilot 4:12 p.m. 3 Americans praised for subduing gunman on European train Giant panda gives birth, National Zoo says
Our new comment system is not supported in IE 7. Please upgrade your browser here.