The forward was injured and left the game during the first minute of the second period of a 3-1 loss at the St. Louis Blues on Monday.
"I should know more early next week, Tuesday, Wednesday," Avalanche coach Jared Bednar said Wednesday. "Just seeing how he progresses over the next few days, I think, is the big thing. I can tell you I don't think it's going to be a 4-6-week injury, I'll give you that. We're hoping he's going to be back significantly sooner than that, but we're just going to have to watch it and see how he's feeling in a couple days and what type of workouts he's going to be able to do and just see how he responds to some of the extra work he gets off the ice to start and then on the ice as well.
"You lose a guy in the middle of the game and he leaves, your mind starts thinking the worst. As of now, to be re-evaluating him again early next week and see how he responds to some of the treatment and whatnot, I think it's a positive, for sure. We're at the point in the season where we want him to come back fully healthy. We don't want him to be out too long either, so there's going to be a little bit of a balance there."
Rantanen is tied with center Nathan MacKinnon for the Avalanche lead with 12 points (five goals, seven assists) in nine games.
"He is one of the best players in the NHL," MacKinnon said. "When you lose one of the best players in the NHL, it's tough. We're not going to replace him, but he got hurt last year and we found a way to get some wins. Hopefully, we can weather the storm until he gets back.
"Mikko is a freak, he will be back, I'm sure, sooner than later, and like I said, we need guys to step up, including myself."
The Avalanche (7-1-1) play the Vegas Golden Knights at T-Mobile Arena on Friday (6 p.m. ET; ESPN+, ATTSN-RM, ALT2, NHL.TV).
"We've dealt with this before, other guys have been hurt," Avalanche captain Gabriel Landeskog said. "It's a team game, it's not a one-man show. We know how important Mikko is for us, no doubt, but that's why we have depth on this team."
NHL.com independent correspondent Rick Sadowski contributed to this report