He was hurt in a 7-1 loss to the U.S. on Thursday.
Marcinko might miss the rest of the season for the team he plays for professionally in Slovakia.
The New York Rangers drafted him in the fourth round in 2006. He played for their affiliate in the American Hockey League, but wasn't called up for an NHL game.
Slovakia is scheduled to play its second of three games in the round-robin preliminary round on Saturday against Slovenia.