The movie, which features the voices of Depp, Isla Fisher and Bill Nighy, follows a group of chameleons searching for water that has been stolen from a town called Dirt.
Throughout the film "at least 60 instances of characters smoking" have been counted, according to Kori Titus, CEO of non-profit organisation Breathe California.
Anti-smoking activists are now claiming the images of animated lizards and birds puffing on cigarettes pose a risk to children, who they claim will want to take up the habit after seeing the footage.
Stanton Glantz, director of the Center for Tobacco Control Research and Education at the University of California-San Francisco, says, "A lot of kids are going to start smoking because of this movie."
Campaigners now want movie chiefs to add a Surgeon General's warning to the project, reports the Sydney Morning Herald.
A spokesperson for movie studio Paramount, Virginia Lam, insists they never meant to condone smoking and they ensured the main character isn't seen puffing away.
She tells USA Today, "The images of smoking in the film... are portrayed by supporting characters and are not intended to be celebrated or emulated."