The Tigers reassigned Vasquez to minor-league camp Thursday.
Vasquez signed a minor-league contract with the Tigers on Thursday that includes an invitation to spring training, Evan Petzold of Detroit Free Press reports.
Vasquez elected to become a free agent Tuesday, Evan Woodbery of MLive.com reports.
Vasquez (calf) was activated from the 15-day injured list Friday, Chris McCosky of The Detroit News reports.
Vasquez was placed on the 15-day injured list Tuesday with left calf tightness, Evan Petzold of the Detroit Free Press reports.
Vasquez, who tossed 1.1 scoreless innings of relief in Friday's 5-2 loss to the Red Sox, has a 2.16 ERA this season.
Detroit claimed Vasquez off waivers from the Phillies on Friday.
The Phillies designated Vasquez for assignment Wednesday.
Vasquez (2-0) earned the win Saturday against the Athletics, striking out two while allowing one hit, one walk and one unearned run over two innings.