The quake hit Yingjiang County at 9:20 am (local time), according to the China Earthquake Networks Centre.
Tremors were strongly felt in the county seat, where residents rushed to open areas for safety, state-run Xinhua news agency reported.
Five of the 29 injured are in a serious condition.
The quake has disrupted electricity supply in Kachang township and Mengnong and Sudian villages, though communications have not been affected, provincial authorities said in a statement.
The Yunnan government has initiated a grade II emergency response, sending a work team of over 50 people for surveying, investigation and disaster evaluation.
The Yunnan Military Area has mobilised over 1,000 soldiers to join in the rescue work, while 1,000 more military officers are preparing to join the efforts.
More than 360 teachers and students from Wupai Primary School in Kachang township have been relocated to safety zones. The school was seriously damaged in a 5.6-magnitude quake that hit the same region a week ago.
The provincial government has sent tents, quilts, folded beds and mattresses to the disaster-stricken region.
Yunnan lies where the Eurasian Plate and Indian Plate meet, and the province is prone to quakes.
Yingjiang borders Myanmar and has a population of 300,000.
In March 2011, the county was jolted by a 5.8-magnitude quake, leaving 26 people dead and over 300 others injured.
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