The theft of the bronze sculpture happened in July but police have just released CCTV footage of the robbery.
It shows two men walking into the Glyptoteket museum and removing The Man with the Broken Nose from its plinth before walking out.
The art work made in 1863 is thought to be worth $300,000 (Â£190,000).
Chief investigator Ove Randrup said the theft of the 25.5cm (10.4-inch) art work happened on 16 July.
Danish police say they believe the thieves visited the museum a week before the theft in order to loosen the sculpture from its base and disable the alarm.
Interpol and Europol have now joined the hunt for the men.
Police in Denmark are hunting for two thieves who stole a small bust by the French sculptor Auguste Rodin from a museum in Copenhagen in broad daylight.