Security forces disrupted Tibetans in Sichuan province's Daofu county as they carried out rituals to honour their exiled leader, whom Beijing denounces as a separatist, said the US-based International Campaign for Tibet (ICT) and India-based phayul.Com.
Regional authorities denied the allegations.
"Two Tibetan monks were shot in the head and several others seriously injured after Chinese police opened fire at a crowd," ICT said, citing unnamed local and exile sources.
Armed police and soldiers who arrived to block the group began shooting and using tear gas "without warning", it said, citing two Tibetans in exile.
More From This Section
At least 20 people were detained after the incident on Saturday, ICT added.
Phayul, a news site on Tibet, said police opened fire after a monk tried to "drive past the security blockade", citing an overseas Tibetan. One monk was shot in the head, Phayul said.
Police and religious affairs authorities in Daofu both told AFP: "There was no incident of this kind".
Members of the ethnic minority have long complained of religious and cultural repression by Beijing, and more than 100 have set themselves on fire in recent years in apparent protest at Chinese rule.
Beijing insists it respects ethnic minorities and has invested heavily to develop Tibetan areas. It blames self-immolations on overseas groups seeking to push a separatist agenda.
Friction in Tibetan areas has sharpened as ethnic majority Han Chinese have increasingly settled in Tibetan areas. Reports of authorities opening fire are rare, however.
The Dalai Lama fled Tibet following a failed uprising against Chinese rule in 1959 and later founded the Tibetan government-in-exile in India.
Last month Beijing denied reports that it had relaxed its policies of publicly denouncing the Dalai Lama and banning worship of his image.