The group, headquartered in London, said the victim, identified as Gepey, died Saturday, the 53rd anniversary of the failed Tibetan uprising against Chinese rule. The 1959 uprising forced Tibetan spiritual leader the Dalai Lama to flee to neighboring India, where he has been living in exile ever since.
Gepey was a monk at the Kirti monastery in Ngaba.
"The monk from Kirti Monastery set himself on fire at around 5 p.m. (local time) on the anniversary of the 1959 Tibetan uprising. He is the 26th Tibetan to self-immolate in the last 12 months," Free Tibet said on its Web site.
Ngaba, which China refers to as Aba, was under heavy security lockdown as the region has a large Tibetan population.
Free Tibet said the self-immolation took place behind the Ngaba County Military camp, adding Gepey was the third Tibetan in a row to self-immolate near the same site.
The group said Chinese authorities refused to allow the traditional funeral rites "for fear that it would give Tibetans a chance to gather and provide an opportunity for further protest against China's repression." The report said Gepey's family was ordered to cremate the body immediately.
Lobsang Yeshi, a representative of Kirti monastery in India, told the Voice of American Gepey is survived by his mother and two brothers who are monks at the same monastery.
This month also marks the anniversary of the protests across Tibet in March 2008.
Leaders of Tibetan exiles and advocacy groups have expressed concern over the worsening situation, urging intervention by the international community.
China accuses the Dalai Lama and Tibetan overseas groups and exiles of encouraging unrest.