"There were two strong bumps, and another three bumps afterwards, lasting around 10 minutes," one passenger on flight MU774 told the Huaxi Metropolis Daily.
Another passenger said an elderly man passed out when he fell onto the floor when his armrest broke.
The crew attended injured passengers while the plane was still in the air by treating wounds with ice packages and putting on bandages.
The cabin broke into a round of applause when the plane landed at 9am - an hour after its scheduled time, another passenger said.
Local authorities in Kunming were "still checking the overall number of injured", Xinhua added in its report late Sunday.
The incident comes after China Eastern Airlines faced criticism after a dog that it was transporting was found dead. It also incensed some Chinese web-users by offering to pay compensation by the kilogram.
The airline made global headlines earlier this month when one of its planes had to turn back to Sydney when a technical problem left a hole in one of the engines.
Additional reporting by Christine Wei