The roster move was backdated to June 6, which means Sanchez is eligible to come off the DL next Sunday, but it's not immediately clear if he'll be ready by then. Sanchez departed Sunday afternoon for Dunedin, Fla., where he will rehab the injury.
Right-hander Scott Copeland is expected to be recalled from Triple-A Buffalo on Monday. He'll get the start against the Mets in New York on Tuesday that originally belonged to Sanchez.
"It's just the right move, smart move," said Blue Jays manager John Gibbons, who added that he hopes Sanchez ends up missing just the minimum 15 days.
The loss of Sanchez for any prolonged period of time would represent a big blow to the Blue Jays' rotation. The rookie starter has become one of the club's most reliable pitchers and allowed three runs or fewer in all but one of his 11 outings this year.
Sanchez's biggest step forward this year came when he started to limit walks. He walked a season-high seven batters on April 22 and issued six free passes during an outing on May 2, but since then the 22-year-old has been much better.
Sanchez decreased his number of walks in four consecutive starts, and during his last outing against the Astros, he didn't walk a single batter over eight-plus innings, which included just one earned run.
Copeland will be returning to the rotation after making a spot start during Sanchez's absence last week. In his first big league start, he allowed one run on six hits without walking a batter in a 7-2 victory over the Marlins on Wednesday.
The 27-year-old was optioned to the Minors following that outing, and normally players cannot return for 10 days but an exception is made when someone goes on the DL.