Four of the five local cases were registered in the city of Ruili while the remaining one was from Longchuan County under Dehong Dai and Jingpo Autonomous Prefecture that borders Myanmar, reports Xinhua news agency.
All the locally transmitted cases were identified in the mass nucleic acid testings.
Three of the imported confirmed cases were from Myanmar between July 3 and 17 while the two others arrived in China from Indonesia on July 16.
All of them tested positive for Covid-19 on Sunday while under quarantine, according to the commission.
The province also reported one imported asymptomatic case.
By the end of Sunday, there were 214 confirmed cases in hospitals in Yunnan, including 74 locally transmitted cases.
There were also 26 asymptomatic cases, including one locally transmitted.
Ruili, which lies along China's border with Myanmar, has been reporting new locally transmitted Covid-19 cases since July 4.