Maile was injured in Thursday's intrasquad game after being hit by a pitch. He had surgery Friday.
The 29-year-old joined the club this offseason on a one-year contract that includes salaries of $900,000 while in the major leagues and $325,000 while in the minors.
A five-year veteran, Maile has played for the Rays and Jays. He is a career .198 hitter and has 10 home runs and 60 RBIs in 215 games.
The Associated Press contributed to this report.