The elephants seen in the video were bathing in the ocean for a cooling dip as part of Cirkus Arena tradition when visiting the coastal city, according to Danish media.
But after workers started rounding up the colossal animals, they appeared to get spooked by the large crowd watching them, as seen in footage caught by tourist Oddmar Nygard last weekend.
The distressed elephants can be seen in Nygard's video getting antsy and aggressively approaching spectators, including an elderly man on a mobile scooter and a woman with a stroller.
A circus worker in a black jacket and brown hat then appears to hit one of the elephants with what looks like a cane, agitating the elephant, which then attacks a nearby unoccupied vehicle.
The elephants were eventually brought under control, Nygard said, adding that they seemed OK at the circus performance the same night.
The damage to the car will be covered by the circus' insurance, Cirkus Arena wrote on its Facebook page.
Cirkus Arena director Benny Berdino has told Danish media he believes the incident is not the circus' responsibility because "people should have kept their distance," though he has said he will request police assistance next year.
Berdino added that he actually believes the incident is funny now that it has ended.
But animal rights activists in Denmark aren't laughing.
"The incident Saturday in which a circus elephant went berserk in Karrebaeksminde shows that wild animals do not belong in the circus, wrote Dyrenes Beskyttelse, an Danish animal rights group whose name translates to "Animal Protection" in English.
The group now has a petition on their site asking Denmark to ban wild animals in circuses.
"It is stressful for wild animals to be transported around," the group wrote on the petition. "The animals are transported, often daily, around in small carts and housed in very cramped conditions.”