Eleven of the injured were in serious condition while 21 sustained minor injuries, state news agency Xinhua reported, citing Nagqu City's emergency management bureau.
Local authorities have found at least two people injured in a village near the epicentre, with some houses in villages closest to the epicentre showing cracks, the state broadcaster said.
The quake is the strongest earthquake in the region in the last five years, China's national broadcaster CCTV said.
The epicentre was in a sparsely populated, high-altitude county in Nagqu, northern Tibet, at a depth of 10km. The average elevation within 5km of the epicentre is about 4864m, China Earthquake Networks Centre (CENC) data showed.
Videos released by local officially run media showed people leaving their homes and seeking shelter outside or in their cars parked on the street. One resident reported being awakened by the strong quake and heard the house squeaking in the tremor.
The quake was clearly felt in the local area, CENC said. The epicentre was around 400km from the Tibetan capital of Lhasa.
Local fire and rescue teams have mobilised and are heading to the affected region, state media said.
A string of smaller tremors of around magnitude three and four have been recorded in surrounding regions following the magnitude seven quake, CENC data showed.
In 2010, a magnitude 7.1 quake struck Yushu in neighbouring Qinghai province, killing at least 2,698 people and leaving nearly 300 people missing.
with AP
30°C