Radio station Europe 1 reported that the man was a neighbour of the dead girl's parents in the small town situated south-east of the city of Nîmes.
The girl, called Océane, went missing on Saturday evening. Her body was found on Sunday morning just two to three kilometres from her family home.
Public prosecutor Robert Gelli told a press conference on Sunday she had been stabbed.
"It's not possible to say at this moment whether she was sexually assaulted," he told journalists. "We'll have to wait for the results of the autopsy."
The alarm was raised by the girl's parents on Saturday evening after she failed to return from a trip to visit a friend who lived nearby.
Forty police officers were involved in a search through the night for the girl which was made more difficult by the torrential rain that has been falling in the region for several days.
Her body was eventually found on Sunday at around 10.30am by one of the 300 people who had responded to a call for volunteers to help with the search.
Local newspaper Midi Libre reported on Monday that she had been stabbed four times.