BEIJING—At least 80 people were killed and more than 700 were injured after several earthquakes, the largest measuring magnitude 5.7, struck southwestern China on Friday, according to local authorities and state media.

The earthquake's damage was heaviest in rural Yiliang county, in a mountainous northeastern part of Yunnan province, near the border with neighboring Guizhou province.

At least one elementary school collapsed in the earthquake, local authorities said, and rescue missions were under way. Authorities said it wasn't clear whether any students had been killed in the quake.

The earthquakes rekindled memories of the 2008 earthquake in Yunnan's neighboring Sichuan province, which left more than 80,000 people dead. Thousands of students then were killed after shoddily built schools collapsed, sparking nationwide outrage toward the government over lax building standards.

Rural Yunnan and Guizhou are among China's poorer regions, and heavily populated by non-Han Chinese ethnic minority groups, such as the Yi and Hui people.