Burrows suffered the injury blocking a shot while killing a two-man advantage in Vancouver's NHL season-opening 4-1 loss to the San Jose Sharks Thursday night.
"Alex Burrows is out and he's probably going to be out for a couple of weeks," head coach John Tortorella said Saturday prior to the Canucks' game against the Edmonton Oilers.
"I know you're probably going to ask about 15 questions about shot blocking. Alex Burrows made the right play and if he doesn't make that play, he'll probably never kill a five-on-three again here. So don't turn it into that. It was the right play to be made. Injuries happen in a lot of different ways."
Tortorella wouldn't give any information on the exact nature of the injury.
"I just don't think we need to give out that information," he said. "He's going to be out for a couple of weeks and that's the way we're going to leave it for right now."
Burrows lead the Canucks with 13 goals last season. He also had 11 assists in 47 games.