The incident happened when Flight MU744 from Charles de Gaulle Airport was descending to land at Kunming Changshui International Airport in Yunnan province, Xinhua news agency reported.
Passengers are being treated for bone fractures, scalp lacerations and soft tissue injuries caused by falling baggage or collisions with overhead lockers, it cited local hospitals as saying.
The nationalities of the injured passengers are unclear.
China Eastern Airlines said on its official microblog account that the company has arranged medical services, without providing other details.
"(We) remind all passengers, for your safety, please fasten safety belts," the post added.
The airline did not respond to questions from AFP.
The plane landed around 9 am (0100 GMT) on Sunday, an hour later than scheduled, according to Xinhua.