Sanchez, 29, had surgery to repair a labrum tear in 2007. He missed less than two weeks with shoulder soreness in spring training last year but otherwise has remained healthy since the surgery. Sanchez threw at least 195 innings each season from 2010-12.
In 12 starts this year, Sanchez has gone 6-5 with a 2.65 ERA and 1.09 WHIP with 11.3 K/9 in 78 innings. He currently ranks to second to Adam Wainwright with 3.4 WAR (FanGraphs version) among all big league pitchers.
Alvarez, 24, went 5-4 with a 2.42 ERA in 12 Triple-A starts before getting the call. He will be making his big-league debut on Sunday after signing as a minor-league free agent during the offseason.
The Tigers acquired Sanchez from the Marlins at the trade deadline last year and re-signed him to a five-year, $80 million contract this winter.