The 55-seat vehicle had 61 people on board when it veered off road and overturned in Gannan Tibetan Autonomous Prefecture at around 1:20 am today, police said.
Among the passengers, 12 were minors, state-run Xinhua news agency reported.
The survivors have been taken to the nearby hospitals. Four people are in critical conditions and put under intensive care, they added.
The bus left Wenshan, southwest China's Yunnan, for Gansu's capital Lanzhou yesterday. The passengers were all migrant workers who were going to work in Lanzhou.