The team also confirmed that forward Aaron Downey has cleared waivers.
It is Leighton's fourth NHL organization this season. He signed as a free agent with Anaheim in July, was claimed on waivers by Nashville on Nov. 27 and was claimed again on waivers by Philadelphia on Jan. 11.
The 25-year-old Petrolia, Ont., native allowed two goals in one period in his only appearance for Nashville and went 2-2 with a 3.70 goals-against average and a .882 save percentage in four games for the Flyers.
He was drafted by Chicago in 1999 and also spent time in the Buffalo system. He has played 47 career NHL games.
The club did not say where Leighton will be assigned.
The Canadiens are missing No. 1 goalie Cristobal Huet, who is out for the season with a torn hamstring, and AHL goalie Yann Danis is out with a neck injury.
Kostitsyn was recalled just one day after being sent down to Hamilton when centre Steve Begin returned to the lineup after missing three games with a broken foot.