The moves Saturday come a day after Reyes was lit up for eight runs in four innings by the Rangers in Toronto's 12-2 loss at Texas.
Reyes has given up 15 runs and 18 hits in his last two starts. The 26-year-old made 20 starts for the Jays this season, going 5-8 record with 5.40 ERA. He joined Toronto last season in a trade with Atlanta.
Ledezma has made 34 relief appearances this season with Las Vegas with a 1-1 record and 4.63 ERA. The 30-year-old left-hander has appeared in 187 games in the majors, including 40 starts, over eight seasons with Detroit, Atlanta, San Diego, Arizona, Washington and Pittsburgh.