The incident happened by the Kirti monastery, in Aba prefecture, in Sichuan province, where many Tibetans live, the London-based group said.
The attempted suicide was confirmed by Radio Free Asia, but the propaganda department of Aba refused to comment.
In the past year, about 30 Tibetans – many of them young Buddhist monks and nuns – have self-immolated to protest against Chinese rule.
In the latest incident, witnesses quoted by Radio Free Asia and Free Tibet said security forces hit the monk while he was alight, before extinguishing the flames and taking him, still alive, to an unknown destination.
Many Tibetans in China complain of religious repression, as well as a gradual erosion of their culture, which they blame on a growing influx of majority Han Chinese in areas where they live.
China, however, denies this and says Tibetans are leading better lives than ever before thanks to huge investment in infrastructure, schools and housing.
Beijing has accused overseas organisations of seeking independence for Tibet and blamed the Dalai Lama – Tibet’s exiled spiritual leader – for the unrest.
Tibet’s government-in-exile said more than 200 people died in the March 2008 unrest, but China denies that account, saying there were 21 deaths and that “rioters” were responsible.
Authorities have mounted a heavy security presence in Tibetan-inhabited areas in response to the self-immolations and sometimes deadly clashes between protesters and police in recent months