China's state Seismological Bureau said the initial earthquake occurred in Dangxiong county, which has a population of about 42,000 people, mostly herdsmen.
"I felt the building shaking a little bit and saw a bench overturn," said Ge San, an employee at the Baima Hotel in Dangxiong, who was sitting in a room with about five other employees.
"The shaking was not heavy. We stayed in the room and were not frightened."
China's far west is quite earthquake prone.
A magnitude-5.7 earthquake shook on Sunday 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.