The 20-year-old Boedker has 12 previous appearances with the Coyotes, with a goal and two assists. He appeared in 78 games as a rookie for Phoenix last season.
Hoggan has four appearances for the Coyotes this season. He had eight goals and four assists in 43 games with San Antonio.
Perrault had just been called up from San Antonio when he suffered an upper body injury in Phoenix's 6-1 victory over Edmonton on Monday night.
Forwards Shane Doan and Vernon Fiddler also had upper body injuries in the game and their playing status was being evaluated on a day-to-day basis.