It's a big blow for the Falcons because Mughelli is a critical piece to the success of running back Michael Turner and the team's ground game.
Fox Sports reporter and NFL Network contributor Jay Glazer first reported the news on Twitter.
Mughelli suffered the season-ending injury to his right knee during the fourth quarter of the Falcons' 23-16 victory over the Detroit Lions when he was hit by defensive back Louis Delmas on a 4-yard reception. It was a rare offensive opportunity for the blocking back, who had just four catches for 25 yards and two touchdowns and two carries for 1 yard this season.
"Jason stepped in (Sunday) into a no-huddle situation where he was playing fullback and we were running our no-huddle offense and we didn't miss a beat," Smith said. "Jason has done it in the past and he's very familiar, and that's one of the reasons we have him on our roster because he gives us flexibility to play both the fullback and the halfback."
With Snelling at fullback, there could be more opportunities for rookie running back Jacquizz Rodgers to play behind Turner.
To replace Mughelli on the roster, the Falcons signed fullback Mike Cox, who was with the team during training camp. Cox originally was signed by the Kansas City Chiefs as a college free agent out of Georgia Tech in 2008 and played in 32 games over three seasons.
The Falcons also placed guard Mike Johnson on IR with a foot injury and signed lineman Kirk Chambers to their active roster. Johnson, a third-round draft pick from Alabama last year, played in two games this season. Chambers played with the Cleveland Browns and Buffalo Bills from 2004 to 2009 and was released by the Lions before the start of this season.
The Associated Press contributed to this report.