Muzzin suffered a fractured foot on Dec. 27 against the New Jersey Devils and has missed the club's last 10 games.
The loan could give the 30-year-old rearguard an opportunity to see game action during the NHL All-Star break, which runs from Jan 23-26. The Marlies play a pair of contests in Cleveland on Friday and Saturday.
Muzzin skated on Jan. 15 for the first time since the injury, and the team hopes he'll be NHL-ready when they return from the break, according to Sportsnet's Chris Johnston.
The Ontario native leads the team in hits (87) and ranks second in blocks (69) despite missing extended time, and he plays a key role on the penalty kill. Offensively, Muzzin has contributed 13 points in 38 games this season.
Toronto is back in action against the Nashville Predators on Monday.