Brand posted bond and was released from jail Thursday afternoon, said police spokesman Frank Robertson. Bond had been set at $5,000, he said.
Police issued the warrant earlier Thursday for Brand, who is in New Orleans to film an untitled movie.
Police spokeswoman Remi Braden on Thursday could not immediately release details of what happened Monday. Celebrity website TMZ said the charges stem from a confrontation with a photographer who was trying to take Brand's photo from a car.
In a Twitter posting on Wednesday, Brand wrote, "Since Steve Jobs died I cannot bear to see anyone use an iphone irreverently, what I did was a tribute to his memory."
Neither Brand nor his publicist could immediately be reached for comment.
Brand's film credits include "Forgetting Sarah Marshall" and "Get Him to the Greek." A judge recently granted him a divorce from singer Katy Perry.
Mandate Pictures, which is producing the untitled comedy in New Orleans, said it is being directed by "Young Adult" and "Juno" writer Diablo Cody.
The film also stars two-time "Dancing With the Stars" champ Julianne Hough, Octavia Spencer, who recently won the Best Supporting Actress Oscar for her role in the movie "The Help," as well as Nick Offerman and Holly Hunter.
