The quakes struck the border of Yunnan and Guizhou provinces, with the largest felt at 11:19 Beijing time, Xinhua news agency said.
The US Geological Survey registered the two strongest of the series of quakes at 5.6 magnitude.
The quakes affected mostly mountainous areas that saw landslides, reports say.
Zhang Junwei, a spokesman from the Yunnan seismological bureau, told the Associated Press (AP) agency that most of the deaths were from Yunnan’s Yiliang county.
“The casualty number is still being compiled. I don’t know what was like for the other towns, but my town got hit badly,” another government official in Yiliang told AP.
No deaths have been reported in Guizhou so far.
The death toll is expected to rise further, especially in areas affected by landslides, Xinhua says.
“Roads are blocked and rescuers have to climb the mountains to reach hard-hit villages,” Li Fuchun, head of Yunnan’s Luozehe town, was quoted as saying.
Xihua reported that at least 100,000 people have been evacuated and earlier reports said that more than 20,000 houses were damaged.
Mobile and regular phone service in the area was experiencing disruption, according to reports.
Hundreds of local residents had gathered on streets littered with bricks and rocks, television footage from state-run broadcaster CCTV showed.
Users of the Twitter-like weibo reported people rushing out of shaking office buildings, and photos posted online also showed streets strewn with rubble.
Local officials said teams had been sent to distribute tents and blankets to those affected.
The largest of the quakes was also felt in the neighboring province of Sichuan, where a 7.8 magnitude quake in 2008 left tens of thousands dead.
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