The 25-year-old Alvarez underwent season-ending shoulder surgery last July.
Alvarez signed a one-year contract with the A's in December after he wasn't offered a contract by the Marlins for the 2016 season.
An NL All-Star in 2014 when he was 12-7 with a career-best 2.65 ERA in 187 innings pitched for Miami, Alvarez went 0-4 with a 6.45 ERA in four starts for Miami last season, which was shortened by two stints on the disabled list for injuries to his right shoulder.
Alvarez is 27-34 with 3.80 ERA in 92 starts in five big league seasons with Toronto and Miami. He pitched a no-hitter against Detroit on the final day of the 2013 season.
Information from The Associated Press was used in this report.