It is the third known case in the NHL after two players for the Ottawa Senators had tested positive.
"The player has been at home in isolation since the first symptoms appeared, and has recovered and is back to normal," the Avalanche said in a statement. "The Avalanche have notified anyone who has had known close contact with the athlete.
"The health and safety of our players, staff, fans, and community remains our highest priority. The Avalanche organization will continue to work in conjunction with our medical staff and public health officials to do everything we can to help the Avalanche community remain safe and healthy during this time."
The NHL's season has been on pause since March 12 and players were told to self-isolate. Four days later, the NHL told players they were allowed to return to their offseason homes or home countries, as long as they self-isolate there.
On Wednesday, NHL chief medical officer Dr. Willem Meeuwisse called it "fortunate" that the NHL had only two positive tests to that point.
"I think we were fortunate in making the decision on March 12 to not only pause play, but actually have players go into self-quarantine, including staff and coaches," Meeuwisse said. "We have a pretty good idea now, because we're almost at the two-week mark, that the likelihood of them being affected prior to that period is pretty low. That doesn't mean someone can't be exposed now."