Toronto infielder Lourdes Gurriel Jr. will also miss the team’s remaining five games with a hamstring injury.
Sanchez was shut down for the season with his troublesome finger on Monday but it wasn’t clear until Tuesday that he would require surgery to repair it.
The 26-year-old sported a 4.89 ERA with 86 strikeouts and 58 walks over 105 innings pitched in 20 starts for the Blue Jays this season.
Gurriel was forced to exit Monday’s game against the Houston Astros with tightness in his left hamstring in the bottom of the first inning.
In 263 plate appearances, the Blue Jays rookie hit .281/.309/.446 with 11 home runs and 35 RBI over 65 games played with the club this season.
Toronto continues its three-game series with the Astros Tuesday, the club’s final homestand of the season, and will close out its season with a weekend series beginning Friday in Tampa.