Barbato signed a minor-league contract with the Blue Jays on June 3 and was assigned to Double-A New Hampshire.
Barbato was outrighted to Triple-A Toledo on Thursday.
Barbato was designated for assignment by the Tigers on Tuesday.
Barbato (shoulder) was reinstated from the 10-day disabled list and sent to Triple-A Toledo on Friday.
Barbato (shoulder) retired two of five hitters and gave up three earned runs on one hit and two walks in his rehab appearance Monday for High-A Lakeland.
Barbato's MRI revealed tendinitis in his rotator cuff, Jason Beck of MLB.com reports.
Barbato was placed on the 10-day disabled list Friday due to shoulder discomfort and will undergo an MRI on Saturday, Evan Woodbery of MLive.com reports.
The Tigers recalled Barbato from Triple-A Toledo on Wednesday.
The Tigers optioned Barbato to Triple-A Toledo following Sunday's 8-4 loss to the Blue Jays, Jason Beck of MLB.com reports.
Barbato was recalled from Triple-A Toledo on Tuesday, Chris McCosky of The Detroit News reports.