The 6.0 magnitude earthquake struck near Yibin in Changning County, south-east of the provincial capital Chengdu, late on Monday, officials said.
It was followed by several powerful aftershocks.
TV footage showed rescuers pulling injured people from the rubble of collapsed buildings.
More than 4,000 people have had to be relocated because their homes were destroyed or damaged, state media reported.
China Central Television showed the aftermath of a landslide that had blocked a road and left a lorry engulfed in debris.
Several major roads were damaged including the highway between Yibin city and Xuyong county, the official Xinhua news agency reported.
In Chengdu, about 300km (186 miles) away, an early warning system triggered a siren that sounded across the city about a minute before the earthquake struck, Xinhua said.
Shaking was felt in Chengdu and also in the city of Chongqing, to the east of Yibin.
More than 500 firefighters have been deployed to the area and rescue teams are bringing in 5,000 tents, 10,000 folding cots and other supplies, the authorities said.
Sichuan is regularly hit by earthquakes.
In 2008 more than 87,000 people were killed in a 7.9 magnitude tremor 80km (50 miles) north-west of Chengdu.
In 2017 a 7.0-magnitude quake also north of Chengdu killed more than 20 people.