Coutu tore the hamstring in his right, kicking leg during Thursday's practice while attempting an onside kick technique that forced him kick almost straight down on the football.
The junior All-America candidate, who hit 7-of-8 field goal attempts this year, watched Saturday's game from the sideline on crutches.
"I feel like I'm a redshirt freshman again, having to watch everybody else play," he said. "It kind of makes you realize how much you love the sport."
Coutu promised a "105 percent recovery." He will begin strength training his leg in two months.
"Since I'm out for the season, there's no rush," he said. "We have to make sure we let it heal."
Coutu was replaced Saturday by junior Andy Bailey, who hit a 22-yard field goal and three extra points in the first half against the Volunteers. Bailey missed one extra point in the second quarter but got a second chance thanks to an offsides penalty on Tennessee. His second chance barely went through the uprights.