More than 120,000 homes sustained significant damage from the temblors, which also triggered massive landslides that crushed houses and cars, and also blocked roadways.
This forced some rescue teams to scale mountains to reach isolated, hard-hit communities.
Officials in Yunnan said that more than 4,300 head of cattle were killed due to collapsed sheds and barns.
Two of the strongest quakes registered magnitudes of 5.7 and 5.6 at 11:19 a.m. and 12:16 p.m., respectively, according to the China Earthquake Networks Center.
Torrential rainfall struck the disaster zone two days later, unleashing flash flooding and mudslides.
Floods washed away dozens of tents and emergency hospital beds, which were set up next to a river, the official Xinhua news agency reported.