Duncan's wife, Maja, and manager, Willy Raine, also were arrested on Saturday, the Canadian Olympic Committee said. Raine was charged with impaired driving, CBC News and the Canadian Press reported.
The three were released on Saturday but restricted from leaving South Korea, CBC reported.
A police official in charge of international crime at Gangwon Provincial Police Agency said on Saturday that a Canadian athlete, his wife and manager had gotten into a car in Pyeongchang that had been left unlocked and unoccupied with the engine running.
The official, who did not identify the suspects by name, said the manager drove off with the car before it was stopped by police. The manager has been charged with drunken driving, the official said.
Once the investigation is complete the results will be sent to the prosecution, the official said, adding that unless the alleged offence was deemed a serious crime, they would be able to leave the country after paying a fine.
In a statement on Saturday, Canadian Olympic Committee CEO Chris Overholt said the Korean police had concluded their investigation and that the team members had been released.
"We expect our athletes and team members to conduct themselves responsibly and in keeping with our Canadian and Olympic values," Mr Overholt said.
"We are deeply disappointed in the behaviours of these individuals."
The Duncans issued a joint statement saying they were deeply sorry.
"We engaged in behaviour that demonstrated poor judgment and was not up to the standards expected of us as Members of the Canadian Olympic Team or as Canadians," they said.
Mr Raine said his actions were "inexcusable".
"Words are not enough to express how sorry I am," he said in his statement, adding he let his teammates down and that he also wanted to apologise to the owner of the vehicle.