The team announced on Monday that Flory's MRI results from earlier in the day show a complete bicep tear.
Alouettes general manager Jim Popp said that Flory will be missed on the field, calling the 37-year-old an "institution at right guard" for Montreal.
"As expected, the results of the MRI are not what we wanted to hear, but are what our medical team suspected," Popp said in a statement. "Injuries are a part of sports and unfortunately, Scott sustained a fluke one."
Popp also said that Flory could undergo surgery as soon as Thursday.
Flory suffered the injury during Friday's 22-14 loss to the Calgary Stampeders at Percival Molson Stadium.
The Regina native has been with the team since 1999, playing his whole CFL career with Montreal. He has spent most of his 15 seasons at right guard for quarterback Anthony Calvillo.
Flory is a three-time Grey Cup champion and nine-time CFL all-star.
The Alouettes are 1-2 on the season. They play Calgary at McMahon Stadium on Saturday.