It is expected Backlund could be out from four to six weeks.
According to Wes Gilbertson of the Calgary Sun, Backlund suffered the injury during the overtime period of Calgary's 4-3 win over Columbus on Thursday night.
The injury is a significant blow to the Flames because Backlund began the season with three goals and one assist in eight games. He also recorded a key game tying goal that salvaged a Flames' point in a 3-2 loss against Vancouver on January 23.
Backlund is the second Flame to be placed on injury reserve this week with a medial collateral ligament injury, joining goaltender Miikka Kiprusoff.
With Backlund injured, the Flames have called up center Ben Street from their American Hockey League affiliate in Abbotsford.
The Flames next play in Vancouver Saturday night.