The move is retroactive to Sunday, when Jackson missed a game against Cleveland following the injury.
"You want to make sure it's right. No sense fooling with it," manager Jim Leyland said. "The way they've got to treat it, it'd probably be five, six days for sure. We just want to make sure that it's done right."
The Tigers recalled outfielder Avisail Garcia from Triple-A Toledo.
Jackson is hitting .272 with a team-high five stolen bases. Garcia hit .319 in 47 at-bats toward the end of last season, playing well enough that he made Detroit's post-season roster. Leyland said Garcia is a candidate to play centre field in Jackson's absence, although Don Kelly started there Monday night against Houston.
Left fielder Andy Dirks could also be moved to centre if needed. One thing Leyland ruled out was the possibility of shifting Torii Hunter from right field to centre.
"We'll have a guy out there who can cover a lot of ground," Leyland said. "Kelly's pretty good at covering a lot of ground — not to the extent of Austin Jackson, obviously — and Garcia will cover a lot of ground when he plays."