The US Geological Survey said the first earthquake in Tibet had a magnitude of 6.6 and struck at 4:30pm (08:30 GMT), 80km west of Lhasa.
About 15 minutes later a 5.1 tremor hit an area approximately 96km west of Lhasa.
The nine bodies, along with 11 seriously injured victims, were found in the ruins of collapsed building in Gedar township in Damxung county, near the epicentre, Xinhua quoted a local official overseeing rescue efforts as saying.
The Chinese agency said historical sites and "key cultural relics" were not damaged.
China's far west is quite earthquake prone.
On Sunday a magnitude-5.7 earthquake shook the Xinjiang region, which borders Tibet, Tajikistan and Kyrgyzstan.
Tibet, a remote, sparsely populated region, has been hit by several moderate earthquakes in recent weeks.
Last month, a magnitude 6 earthquake struck near its border with Nepal but there were no reports of damage or casualties.
Monday's quake in Tibet comes just months after the massive quake in China's Sichuan province, which killed at least 80,000 and devastated whole towns and villages in May.