Residents of Tanzania’s main city found them in a shallow pit about 100m from Mwananyamala Hospital on Monday.
Some of the corpses were wrapped in a sheet belonging to the hospital.
The BBC’s Hassan Mhelela in Dar es Salaam says one person is in custody on suspicion of being involved in the incident which has shocked the nation.
It is the first discovery of its kind and is dominating talk shows on the radio, our reporter says.
Amuri Mbaga, the owner of the property where the bodies were found, said he was doing routine cleaning of his compound when he became suspicious that there was something unusual in the rubbish dump.
“I decided to get closer for a look and it was then that I saw the body of an infant that was not fully covered; then we discovered there were 10 bodies in the pit,” he told the BBC’s Focus on Africa programme.
Officials say the investigation is focusing on the likelihood that relatives of the deceased babies chose to pay other people to bury the bodies.
Sophinias Ngonyani, head doctor at Mwananyamala Hospital, said most of the babies were stillborn.
“All procedures were followed before handing over the bodies to the relatives, we don’t know what happened thereafter,” he told the BBC.
Regional police commander Charles Kenyela said a special committee had been set up to deal with the inquiry and it would report on its findings within seven days.
Source: BBC