The Get Him To The Greek star was walking through airport security with his fiancee Katy Perry to catch an afternoon flight out of the city when he became enraged by the snappers blocking his path.
In video footage posted on TMZ.com, Brand can be seen pushing through a throng of photographers before seemingly shoving one paparazzo out of the way.
The website claims a snapper made a citizen's arrest and restrained the star until cops arrived to take control of the situation.
A police statement issued by authorities on Friday claims LAX officers responded to a "report of a battery involving a celebrity and a commercial photographer", prompting the alleged victim to make a "private person's arrest".
Brand, 35, was taken into custody and was subsequently booked for battery.
Ironically, the funnyman was wearing a T-shirt bearing the phrase, "God, come on, give me a break".
A representative for the star has yet to comment on the reports.