With Andersen sidelined, Michael Hutchinson will serve as Toronto's starting goaltender.
In addition to the goaltending change, the Maple Leafs are adjusting their forward lines. John Tavares will be slotting in on the top line alongside Auston Matthews and Mitchell Marner.
It was not immediately clear when Andersen, who has won his last two starts including a 5-3 win over the Montreal Canadiens on Saturday, sustained the injury.
The 31-year-old has an 11-3-2 record this season with a 2.69 goals-against average and a .905 save percentage.
Hutchinson won his first appearance of the season on Feb. 18 against the Ottawa Senators, stopping 34 of 37 shots he faced in a 7-3 win.
The Flames will be without their starting goaltender tonight as well, with Jacob Markstrom sidelined due to an upper-body injury. Backup goaltender David Rittich will be in net instead for the Flames.
Andersen's injury is the latest in a string of Maple Leafs ailments.
Defenceman Jake Muzzin has a broken bone in his face and will miss Monday's game, while forwards Zach Hyman and Joe Thornton will also be sidelined and are considered day-to-day.