The inquiry into the incident at the facility in the 13th arrondissement was announced by Bertrand Delanoë, city mayor.
The baby was found semi-conscious at 8am next to a three-year-old boy before later dying.
Investigators will be looking at the possibility that the boy threw the infant to the ground, according to press reports.
“I want to express my distress after this dramatic death of an infant aged one month this morning at the Michelet nursery,” Delanoë said in a statement issued shortly after the discovery.
Bite marks were discovered on the victim, a police source said, Le Parisien reported on its website.
An autopsy was to be conducted on Monday.
The incident raises questions about the management of the nursery.
Delanoë has demanded that an administrative inquiry be “immediately begun”.
“I offer my personal support to staff at the Michelet nursery, whom I know are particularly affected by this terrible event,” the mayor said.
Despite the seriousness of the incident, Delanoë said the nursery’s employees needed “to be able to continue their work in the calmest environment possible in the overriding interest of the infants and their families”.
The mayor also addressed his condolences to the victim’s family.
Known by its full name as the Michelet de la Dases nursery, the establishment looks after infants and children in difficulty or danger.
The children are either left by family members or ordered there for their protection by social agencies.