The former heavyweight boxing champion and photographer Tony Echevarria, 50, want to press charges of misdemeanor battery against each other, police said.
The photographer told police that Tyson struck him once, airport police spokesman Sgt. Jim Holcomb said. The photographer fell to the ground and was treated for a cut to his forehead at a hospital.
Tyson's spokeswoman Tammy Brook said the boxer was traveling with his wife and 10-month-old child when he was attacked by an overly aggressive paparazzo. "Mike acted in self defense as a father protecting his child," she said.
"There's a lot of different versions to this story and that's all going to come out later," Holcomb said. "Some witness statements support Tyson's version, others support the photographer's."
Police also were checking if there was any surveillance video of the incident.
Tyson was cooperative as he waited in a holding cell at the airport police station, Holcomb said. Echevarria was booked and released after he was treated at a hospital, police said.
Holcomb said both men were released without any restrictions and free to go wherever they want. It wasn't immediately clear if Tyson had continued his trip.
Paparazzi often camp out at Los Angeles' largest airport to get shots of celebrities in transit.
"I've heard people were following him into the men's room and trying to take his picture there," said Tyson's defense attorney, David Chesnoff. "My advice to him is going to be to vigorously press charges against what everyone agrees are ridiculously aggressive photographers."
Tyson became the youngest heavyweight champion ever in 1986 when he won his title as a 20-year-old. But his life since then has been marred by accusations of domestic violence, rape and cocaine use.
Tyson was convicted of rape in Indiana in 1992 and served three years in prison. He was disqualified from a 1997 heavyweight title fight when he bit off part of Evander Holyfield's right ear, and in 1999 he pleaded no contest to misdemeanor assault charges in Maryland.
In 2003, Tyson filed for Chapter 11 protection in U.S. Bankruptcy Court. He served 24 hours in an Arizona jail in 2007 after pleading guilty to cocaine possession and driving under the influence.