He was released from jail soon after, for $5,000 (£3,184) in bail, said police spokesman Frank Robertson.
Reports say Brand, 36, who is in New Orleans filming an untitled movie, had a confrontation with a photographer who was trying to take his picture from a car.
Police had issued a warrant for Brand’s arrest on a charge of simple criminal damage to property valued at $700 (£445) after the photographer accused him of grabbing his iPhone and throwing it through a window.
Brand tweeted on Wednesday: “”Since Steve Jobs died I cannot bear to see anyone use an iPhone irreverently, what I did was a tribute to his memory.”
Brand is filming with Young Adult and Juno writer Diablo Cody for a movie that will be produced by Mandate Pictures.
The film also features Dancing With the Stars champion Julianne Hough and The Help’s Oscar winner Octavia Spencer.
The Essex-born star married singer Katy Perry in October 2010 but they split in December 2011, after just over a year of marriage.
Brand was also arrested at an airport in Los Angeles in 2012 after an alleged attack on a photographer.