Sanchez, who is 3-5 with a 4.52 ERA and 67 strikeouts this season, revealed Wednesday that he suffered a bruised right index finger on June 21, when it got caught in a falling suitcase.
This wasn't Sanchez's first struggle with an injury to his pitching hand. He endured multiple stints on the DL because of blister and fingernail issues last season, pitching just 36 innings over eight starts.
To make room on the roster, the Blue Jays designated left-hander Jaime García for assignment.
The Associated Press contributed to this report.