The monk set himself ablaze in a public square on Saturday morning in Kardze, also known as Ganzi, in western Sichuan province, according to Radio Free Asia and Free Tibet, an advocacy group based in Britain.
The unidentified monk was taken away after the fire was extinguished by security forces, reports said. It was unclear if he survived.
A man who answered the phone at the local police station Monday said he was unaware of the case and "not clear" about the situation. The government for Garze Tibetan Autonomous Prefecture, which includes the town of Kardze, referred questions to police.
Free Tibet acquired the video from a witness who posted it on social media, according to John Jones, a spokesman for the group.
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If the self-immolation is confirmed, it would be the 148th recorded case of a Tibetan self-immolating since 2009, according to Radio Free Asia and Free Tibet. At least 125 have died, according to monitoring groups.
China claims Tibet has been part of its territory for more than seven centuries and regards the Dalia Lama, Tibet's exiled Buddhist leader, as a dangerous separatist. Many Tibetans insist they were essentially independent for most of that time and have protested what they regard as China's heavy-handed rule.
Before lighting themselves on fire, many cried out for Tibetan independence or prayed for the return of the Dalai Lama, who fled Tibet in 1959, eyewitnesses have been quoted as saying.
The most recent previous incident, also in Kardze, was in mid-March, when a Tibetan man identified by monitors as Pema Gyaltsen set himself on fire. Jones said Monday that the 24- year-old farmer's fate remains unknown.