Willis injured the knee while delivering a pitch in the first inning Friday night against the Chicago White Sox and minutes later was taken out of the game.
"We know he's going to miss at least one start and we don't want to take any chances with it," Detroit general manager Dave Dombrowski said after a 7-0 loss to the White Sox on Saturday.
"Really at this point, we can't. It is a hyperextension, so hopefully after the 15 days he'll be ready. But we'll see."
Willis, who joined the Tigers along with Miguel Cabrera in a major trade from Florida, was making his second start Friday night for the Tigers on Friday night.
On his first pitch to the White Sox's No. 2 hitter Orlando Cabrera, Willis' right leg gave out and he slipped off the mound. He stayed in the game, but after walking Cabrera and throwing a wild pitch to Jim Thome, he was taken out. Following the game, Willis said he initially thought he'd blown his knee out, but later was able to put pressure on it.
"There is no tear, so that's good," Willis said Saturday. "We'll see how I feel tomorrow. I'll take it day-by-day. I felt better today, just a little stiffness."
Willis said it was a new experience.
"I never had anything happen like that. But it could have been a lot worse."
The Tigers have been banged up all season and gotten off to a surprisingly bad start.
Center fielder and leadoff hitter Curtis Granderson is out with a broken hand, reliever Fernando Rodney has a tender shoulder and first baseman Carlos Guillen missed Saturday's loss to the White Sox after straining a hamstring while running to first Friday night.
Gary Sheffield has been bothered by a torn tendon in his finger and Cabrera by a sore quadriceps muscle.
Detroit is off to a 2-9 start.
The Tigers will recall outfielder Ryan Raburn from Triple-A Toledo to fill the roster spot and later will bring up right-hander Armando Galarraga, also from Triple-A, to take Willis' slot in the rotation.