The 24-year-old, who will join Edinburgh Rugby in the summer, was injured in last month's Six Nations defeat by England at Twickenham.
Fellow Glasgow Warrior Josh Strauss is expected to be out for six weeks after injuring a kidney on Scotland duty.
Strauss will sign for Sale Sharks on a three-year contract in the summer.
Bennett had anterior cruciate ligament reconstruction surgery and is expected to take between nine to 12 months to return to full fitness.
Back-rower Strauss has been out since February but, following a review by his consultant, the 30-year-old has been told he requires six more weeks of non-contact work before being allowed to return to full training.
"We're disappointed that Mark's time at the club has come to an end in this way, and it also looks like Josh may not play for us again as he continues his graduated return to training," said Glasgow Warriors head coach Gregor Townsend, who is leaving to become Scotland coach.
"We wish both players all the best with their rehab and look forward to having them as part of our wider group for the remainder of the season."
Both players are due to attend Glasgow's Pro 12 game at Scotstoun a week on Friday, along with other squad members who are leaving in the summer, to mark their contribution to the club.
Scotland and Glasgow Warriors centre Mark Bennett faces up to 12 months on the sidelines after having cruciate ligament surgery.