"He has a significant injury," said Wren of Gearrin's condition.
Atlanta will recall left-hander Ryan Buchter back from Triple-A Gwinnett and place Gearrin on the 15-day disabled list. The organization has been looking for outside help, but Wren said he has not found an available player he likes better than the club's internal options.
Gearrin, who left a 12-3 win against the Tigers in Lakeland, Fla., on March 25 after throwing an errant pitch, is one of several Braves hurlers to consult with Dr. Andrews this spring.
Starters Kris Medlen and Brandon Beachy are both done for the season after undergoing Tommy John surgery. Reliever Jonny Venters and starter Gavin Floyd are both in the recovery stages of previous Tommy John surgeries.
"We've kind of eaten through our depth," Wren said. "We felt like we were in pretty good shape coming into Spring Training with some guys about to get healthy, and all of a sudden, next thing you know, we're pretty thin."
Although Atlanta has been hit especially hard with pitcher injuries this spring, Wren recognizes that the Braves are far from the only club with rotation depth issues.
"We always find a way to do it and get over it," Braves manager Fredi Gonzalez said. "Somebody else will step up. I have the confidence in our club that they'll overcome that."
"When I look around baseball, there's a lot of us like this," Wren said. "It's just been one of those springs. There's not a whole lot you can do about it."
Former Braves manager Bobby Cox admits he doesn't know what's causing the injuries, but he has noticed at the Little League, high school and college levels, an intense focus on pitch velocity might be a cause.
"It's velocity, velocity, velocity," Cox said. "My opinion is I think most of them are trying to throw too hard right now."