In exchange, Seattle will receive a player to be named or cash considerations.
Walker is 2-2 with a 4.00 ERA in five starts this season. He has a career record of 33-33 with a 3.95 ERA in eight major league seasons. He made just one appearance last season with the Arizona Diamondbacks while recovering from elbow surgery.
The trade was announced Thursday morning, about three hours before Walker had been scheduled to start the first game of a doubleheader against the San Diego Padres.
He will be a free agent after the 2020 season, for which he is making $740,000 for the 60 games.
Toronto is 15-14 through Wednesday's games and is contending for the final American League spot in the expanded 16-team playoff tournament.
The 28-year-old Walker on Wednesday stood up in an emotional meeting, explaining why he believed it was necessary for the Mariners not to play. Seattle's players decided unanimously to skip the game against the Padres at Petco Park in the wake of the weekend shooting by police of Jacob Blake, a Black man, in Wisconsin.
"Glad to be apart of this organization and group of people!" Walker tweeted Wednesday night after the Mariners made the decision not to play. "Thank you for standing with us always!!"
The Blue Jays put starting pitcher Matt Shoemaker on the 10-day injured list Sunday with a lat strain. He is considered week-to-week.
ESPN's Jeff Passan contributed to this report.