About 100,000 people were forced to evacuate after the quakes.
Some Chinese media reports said at least 150 people were injured.
The U.S. Geological Survey reported four earthquakes around the city of Jiaokui in Yunnan province. Two measured 5.6-magnitude and two 4.8.
The quakes also caused damage in neighboring Guizhou province.
President Hu Jintao, who was in the Russian city of Vladivostok for an economic conference, urged Chinese officials to do their utmost to prevent further injuries and property loss, Xinhua, the official government news agency, said.
Prime Minister Wen Jiabao was on his way to the quake-stricken area.
Workers accuse National Zoo of animal mismanagement
Wisconsin business offering 'therapeutic cuddling' forced to close