Duffy suffered the injury covering first base on Sunday. He tumbled to the ground on the play.
Duffy is 4-4 with a 3.54 ERA and leads the Royals in innings pitched. The 28-year-old has spent his entire seven-year career with Kansas City.
The Royals also announced that Eric Skoglund will start against the Tigers Tuesday, making his major league debut.
Kansas City didn't make the playoffs last season after winning the World Series in 2015 and losing it in 2014. They are 21-28 this season and in last place in the AL Central.