The left-hander suffered the injury during the first inning Friday in his start against the White Sox in Chicago. Willis, 26, slipped on his delivery to Orlando Cabrera, the game's second batter.
He was pulled after surrendering two walks and falling behind in the count to Jim Thome.
"You know he's going to miss a start, and we don't want to take any chances with it," said President-General Manager Dave Dombrowski on the Tigers' Web site. "It is a hyperextension, so hopefully in the 15 days, he'll be ready, but we'll see."
It is the first trip to the DL for Willis, who has never missed any of his 164 starting assignments in his six-year major league career.
"There's no tear, so that's good," said Willis, who came to Detroit in an off-season trade with the Florida Marlins.
2014: The Year in Music [PHOTOS]