The Blue Jays also designated righty Daniel Farquhar for assignment on Saturday.
The 25-year-old Schwinden made two starts and one relief appearance for the Mets this season, going 0-1 with a 12.46 ERA. He is 0-3 with a 6.98 ERA overall in the majors.
Schwinden was 3-4 with a 2.59 ERA with Triple-A Buffalo. The Blue Jays assigned him to Triple-A Las Vegas.
Farquhar was 0-1 with one save and a 2.97 ERA for Double-A New Hampshire. The 20-year-old was 0-0 with a 13.50 ERA in three games for Toronto last year.