Konz is Atlanta's fourth starting offensive lineman to suffer a season-ending injury.
Konz hurt his knee in the Falcons' 29-7 loss at Baltimore on Sunday. Rookie James Stone, who signed with the team in May as an undrafted free agent from Tennessee, took over for Konz and looks like the presumptive starter moving forward.
"It was time to get out there, do my job," Stone said. "That's why we're all out here, to play football. I go out there with those guys and play at the highest level I can."
Atlanta's patchwork offensive line struggled against Baltimore. Matt Ryan was sacked five times.
"We had way too much pressure," coach Mike Smith said. "Our quarterback was hit and sacked way too much. There were times where we really didn't have a chance to get the play off, and that's very difficult for a quarterback, and we have to do better with our protection."
Smith said he wouldn't use injuries as an excuse for the team's fourth straight loss.
"There are no excuses," he said. "You can talk about losing players, but everybody loses players. It's got to be the `next man up' mentality. The next guy up has to step in and do the job. We have to step up and make those plays."
Atlanta signed offensive tackle Jonathan Scott to the 53-man active roster on Monday.
Konz, a second-round pick from Wisconsin in 2012, has made 27 starts at center and right guard.
Scott has 35 career starts with the Lions, Bills, Steelers and Bears in eight seasons.
The loss to the Ravens left the Falcons at 2-5. Following the game, the team flew to London, where Atlanta will play the Detroit Lions on Sunday in a difficult matchup for the offensive line.
"We have nine games left and I know every man in that room and every coach in that room will work ... this week to get prepared to play the Detroit Lions," Smith said. "I have no doubt what the makeup of these football players and coaches and the organization we have in Atlanta."