The move is retroactive to last Friday, the day after Coke took an extra-inning loss to the Royals.
"We can backdate it some, get him better and move on," Tigers manager Jim Leyland said.
To take his place in the bullpen, Detroit recalled right-handed reliever Jose Ortega from Triple-A Toledo. Filling Coke's spot in the bullpen has already proven more complicated.
Drew Smyly, a starting candidate who originally became a long reliever, has transitioned to setup work to fill the void in lefty relief, including back-to-back eighth-inning appearances the past two nights. Ortega essentially fills the long-relief role and lets Leyland focus Smyly on the late innings, alongside fellow southpaw Darin Downs.
Neither Smyly nor Downs has the experience of Coke, the primary left-hander in Detroit's bullpen for most of the past three seasons. Coke felt the groin strain in his most recent outing, when he walked in the go-ahead run in the 10th inning.
In the days since, Coke has tried to get back into action, only to find himself unable to pitch pain free. The latest effort came Tuesday during batting practice, when Coke tried to throw off flat ground. He walked back to the clubhouse with head athletic trainer Kevin Rand and didn't come back out.
Coke will stay back when the Tigers hit the road this weekend and work out in Toledo.
The 24-year-old Ortega made an impression in Spring Training and has posted dominant stats out of the bullpen at Toledo, allowing one unearned run on five hits over 14 innings, with seven walks and 19 strikeouts.
"He's really throwing well," Leyland said. "He's always had electric stuff, and I'm anxious to see him."
That electric stuff so far hasn't translated to Major League success in his brief stints in Detroit, mainly because of command.
"He's been [behind] too many guys. No matter how good of an arm you've got, that normally doesn't work," Leyland said. "We'll see if he can translate what he was doing down there up to the Majors. If he can, that would be a big help, because he's got electric stuff."