According to the Toulouse prosecutor, the player hit a car and attempted to flee but was caught by the car's driver. A fight between the pair started around 0300 local time (0100 GMT), Michel Valet said.
"When the police intervened, they saw that the motorist that had caused the crash was a famous rugby player," Valet said. "And it was clear that he had been taking alcohol."
Police on the scene were unable to test Kelleher's alcohol level because he was too drunk to blow into the breathalyzer, Valet said.
The prosecutor said that other people were involved in the fight that followed the crash and that an investigation had been started.
The 32-year-old Kelleher, who was still in custody this morning (NZT), was not expected to play for Toulouse against Albi in the French League on Saturday.
Kelleher, who joined Toulouse in 2007, played 57 tests between 1999 and 2007 with the All Blacks. He won the French League title with Toulouse in 2008.
