The film has been in limbo amid Gibson's custody battle with ex-girlfriend Oksana Grigorieva, who claims he physically abused her.
"The Beaver" is directed by Jodie Foster and stars Gibson as a troubled family man trying to cope with help from an unusual friend -- a beaver puppet he wears on his hand.
Foster co-stars, along with Anton Yelchin and Jennifer Lawrence. Gibson and Foster previously co-starred in the Western comedy "Maverick."