The cast and crew were filming a dramatic final scene, which features Jackman's PT Barnum carrying his assistant (Efron) from a burning house, in a specially constructed building, reported People magazine.
"There was a small fire on the set of 'The Greatest Showman'. The fire was quickly contained and no one was injured. The main cast had already wrapped when the fire occurred," a representative for movie studio 20th Century Fox said in a statement.
According to the New York Post, around 150 people were on set when six large lights intended to boost the glow of a fire fell from the roof of the building, causing the blaze to spiral out of control.