Avalanche coach Jared Bednar announced the news Friday after practice. He called missing Landeskog a "huge loss."
The All-Star forward was hurt in the third period Thursday at Dallas when he collided with Stars goaltender Ben Bishop.
Landeskog has a career-best 33 goals this season, including an NHL-leading 19 in the third period.
The 26-year-old Landeskog was the second overall pick by Colorado in 2011. He has 410 career points, becoming the second player in his draft class to reach the 400-point milestone.
Colorado is currently on the outside of the playoff picture with 14 games remaining. The team hosts Buffalo on Saturday.