The plane landed around 9am local time (2am Irish time), an hour later than scheduled, according to Xinhua.
Xinhua said (in Chinese) that two violent bumps and many small bumps occurred over about 10 minutes.
During that time, passengers suffered broken bones, cuts and other injuries as some hit the overhead bins and others were struck by falling luggage, according to state news agency Xinhua.
The flight crew took necessary measures and the flight landed safely, China Eastern said in a statement on Sunday morning.
The nationalities of the injured passengers are unclear.
"I was on the flight, and I felt like I would not survive", the SCMP quotes one passenger writing on Weibo.
None of the injured are in critical condition. Baggages fell on many of them as well.
Another middle-aged male passenger told Pear Video that he saw lightning strike outside the aircraft as the turbulence took place. It added that all passengers should fasten safety belts during flights for safety.
China Eastern Airlines made headlines last week after a flight from Sydney to Shanghai was forced to make an emergency landing after an engine became damaged shortly after takeoff. No one aboard the twin-engine Airbus A330 was injured.