The Tigers also promoted relievers Guido Knudson and Jose Valdez from Triple-A Toledo on Thursday.
Detroit sent cash to the Blue Jays for the 38-year-old Wolf. He'll start Saturday against Texas.
Wolf was 9-2 with a 2.58 ERA at Triple-A Buffalo. He last pitched in the majors with Miami last season.
Norris strained his oblique Wednesday against the Cubs at Wrigley Field. The 22-year-old righty homered in his first professional at-bat, but later hurt himself pitching.
Norris was acquired from Toronto in the trade for David Price last month. He is 2-2 with a 4.43 ERA overall.
Sanchez is out with a strained right rotator cuff, an injury that has lingered.
Sanchez is 10-10 with a 4.99 ERA. He has allowed a major league-leading 29 home runs in 157 innings after giving up just four in 126 innings last year.