Italian forward Joachim Ramoser made knee-on-knee contact with Burrows in Canada's offensive zone with 56 seconds left in the first period.
Burrows, who plays for the Vancouver Canucks, was down on the ice in a lot of pain before being attended to by trainers and helped off the ice.
The 33-year-old Burrows was not able to put any pressure on his right leg as he was helped off by Brayden Schenn and Nathan MacKinnon.
Ramoser was given a five-minute major penalty and an automatic game misconduct.
A Hockey Canada spokesman said early in the second period that Burrows was out of the game with a lower-body injury and was being evaluated.
It's the second straight year a Canadian player was the victim of a knee-on-knee hit at this tournament. Eric Staal was on the receiving end of one in the quarter-final in 2013 against Sweden, suffering a sprained MCL.
Alex Edler was suspended the remainder of that tournament and then the first two games of the Sochi Olympics for injuring Staal.
Ramoser's hit will be subject to review by the IIHF, though replays made it look like the contact was not intentional.