The incident, the first immolation since April, occurred Sep 17 but did not come to light until the weekend due to government restrictions on such news, the newspaper said, citing information from pro-Tibetan organisations such as Free Tibet.
The deceased, a student named Lhamo Tashi, set himself ablaze in front of a police station in Hezou, a Tibetan area in Gansu province.
He died immediately and was cremated by the authorities despite his family's demands for the body, the reports said.
According to independent estimates, it was the first immolation in five months since the death of a Tibetan man in Sichuan province bordering Tibet.
A year ago Chinese police in the same region opened fire on followers of the supreme Tibetan Buddhist religious leader, the Dalai Lama, who were celebrating his 78th birthday.
Seven people were injured, according to Tibetan exile sources.
According to the sources, since 2009 there have been about 130 immolation cases against Chinese control of Tibetan areas and in support of the return of the Dalai Lama who has lived in exile in India since 1959.
In June, the Dalai Lama warned that such actions had "very little effect" on China's policy in Tibet and urged Beijing to examine the reasons for the protests.
China claims that Tibet has been an inseparable part of its territory for centuries while the Tibetans argue that the area was independent before Communist troops occupied it in 1951.