Teahen suffered the injury fielding a ground ball on Sunday in Tampa. The move is retroactive to May 31. He is batting .255 with three home runs and 14 RBIs in 45 games and has hit safely in 11 of his last 12 games.
"It sucks, that's pretty accurate," Teahen said. "I felt like I was starting to come around and do what I was brought here to do, and obviously I got to take a little break from that, but hopefully it's not too long."
Sox general manager Ken Williams expects Teahen to be out for a month.
"He's four weeks at least away before he starts to play again, so we got to make do without him," he said.
Lillibridge is hitting. 270 with four home runs and 16 RBIs for Charlotte.
"I don't expect to be like some huge sparkplug for the team, but whatever I can do to make Ozzie [Guillen's] life easier and whether it's pinch running or all that stuff -- do what I did last year hopefully -- but definitely can hit a lot better," he said.
Information from The Associated Press and ESPNChicago.com's Kevin Ware was used in this report.