The incident occurred at about 1:50 p.m. inside terminal 5.
The 35-year-old star was taken into custody and booked on a misdemeanor charge of simple battery. His bail was set at $20,000.
Los Angeles Airport Police spokeswoman Belinda Nettles said the victim, a paparazzo who was not identified, placed Brand under citizen's arrest.
Brand was with his fiance, singer Katy Perry, at the time. Perry later said he had tried to protect her from the photographer.
So far, there is no comment from Brand.
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