The monk, named Tapey, is said to have shouted slogans and waved a Tibetan flag, then doused himself with petrol and set himself alight.
Campaign groups said witnesses then saw Chinese police shoot the man.
The monk collapsed and was taken away by the police.
China's official Xinhua news agency confirmed a man had set himself on fire, saying he was taken to a hospital and treated for burns injuries. It made no mention of any gunshot wounds.
The protest began after more than 1,000 Tibetan Buddhist monks gathered at a temple in the town to celebrate the third day of the Tibetan new year.
Chinese officials had earlier banned the gathering.
After the incident, news agencies reported a heavy police presence on the streets of the town.
"There are many policemen on patrol in the street and all of them have guns," an employee at a teahouse in Aba told the AFP news agency.
It is extremely difficult to independently confirm any information coming out of Tibetan areas.
China's authorities have restricted access to the region.
Next month marks the 50th anniversary of the escape into exile of the Dalai Lama and China wants to make sure there are no Tibetan protests in support of the exiled spiritual leader like those of a year ago, says the BBC's James Reynolds in Beijing.
More than 200 Tibetans are thought to have been killed in a Chinese crackdown in the region, which it has ruled since an invasion in 1950.
China claims Tibet is part of its historic territory, but Tibetan groups in exile regard the invasion as a tragedy.