The move was expected after the Falcons lost starting left tackle Sam Baker to a season-ending patellar tendon tear.
The Falcons drafted Matthews with the sixth overall pick out of Texas A&M to be the team's left tackle of the future. He played left tackle last year with the Aggies.
Matthews was asked after Monday's practice if there is a significant adjustment from right to left.
"Yes, the stagger changes," he said. "You go for a long time used to bracing a guy with one leg back. And now you've got to flip it around. It's like almost going from writing with your right hand to your left hand. But I did it in college. I feel pretty comfortable on both sides."
Said coach Mike Smith: "I don't think he'll blink. We're not."
Lamar Holmes moved into the first-team right tackle spot vacated by Matthews.
The Falcons officially placed Baker on injured reserve Monday and signed veteran offensive tackle Pat McQuistan, who last played with Tennessee. McQuistan has 11 career starts and played eight previous seasons with the Cowboys, Saints, Dolphins, Cardinals, and Titans.