Her body was cremated four hours later and returned to her family, the news agency said, adding that local government officials were investigating.
More than 90 Tibetans have set themselves ablaze since 2009 to protest China's rule of the Tibetan plateau, rights groups have said, with the frequency of incidents increasing sharply in November. Most have died.
According to a partial list drawn up by the London-based campaign group Free Tibet the teenager is among the youngest girls to have set themselves on fire.
Xinhua reported on Sunday that a monk and his nephew had been detained for inciting eight Tibetans to set themselves alight.
Many Tibetans in China accuse the government of religious repression and eroding their culture, as the country's majority Han ethnic group increasingly moves into historically minority areas.
Beijing rejects this, saying Tibetans enjoy religious freedom. The government points to huge on-going investment it says has brought modernisation and a better standard of living to Tibet.