The former heavyweight boxing champion was detained on suspicion of battery following the scuffle at Los Angeles International Airport, police said.
The snapper, who was treated in hospital for a cut to his forehead, told officers that Tyson struck him once, an airport police spokesman said.
“There’s a lot of different versions to this story and that’s all going to come out later,” Sergeant Jim Holcomb added.
“There were numerous witnesses and that’s what this whole case is going to depend on.”
Tyson’s spokeswoman said the boxer, who was travelling with his wife and 10-month-old child, was reacting to an overly aggressive photographer to protect his baby.
Tyson was protecting wife Lakiha Spicer and daughter Milan, his spokeswoman said
The 43-year-old is expected to be released from custody later. The photographer is also likely to be charged, police said.