The official Xinhua News Agency said there were also foetuses among the bodies.
Harry Fawcett, Al Jazeera's correspondent in Jining, said: "This very grizzly discovery was made under a bridge on the outskirts of Jining.
"There is a great deal more still to come out on this story which is certainly receiving a lot of play [in the media] here in China.
"These sort of scandals ... result often in action from local government officials who want to be seen to act."
Tags on the feet of eight of the babies traced them back to a hospital in Jining, according to the People's Daily website.
Three of them had been admitted earlier to the hospital in critical condition, the report said. The other 13 bodies were unidentified.
The number of girls or boys was not reported.
More girls than boys are aborted in China because of the traditional preference for male offspring, especially in rural areas.
Although gender-selection abortions are illegal in China, the practice remains widespread and has led to a skewed sex ratio at birth in China with 119 males born for every 100 females.
In industrialised countries, the average ratio is 107 to 100.
An official from the general office of the Affiliated Hospital of Jining Medical College confirmed it was involved.
"Several of the bodies of babies with [identification] tags were from our hospital, but not all of them," said the official, speaking on condition of anonymity.
"The officials from the health bureau are still in the hospital doing an investigation".
Xinhua said medical staff were suspended after the discovery.
"The hospital medical staff involved have been suspended from their work during the investigation," Zhong Haitao, a spokesman at the Jining Health Bureau, was quoted as saying.
Local residents and firefighters recovered the bodies on Monday after they were discovered under a bridge spanning the Guangfu River in the outskirts of Jining, Zhong said.
Interviews with residents who discovered the bodies floating near the shore over the weekend were broadcast on the website of the Shandong Broadcasting Company, IQILU.com.
The footage shows bodies, some uncovered and others in bags, lying on parts of the bank of the river, many covered in dirt.
One of the bluish-green identification tags visible in the video indicates the baby was born in April 2009.
People's Daily said all the bodies were of babies, while Xinhua said several were foetuses.
An official from the information office of China's health ministry said she was not aware of the case.