Kulak signed a three-year, $5.55 million contract with the Canadiens on Saturday.
Kulak's second-period goal was ruled no goal on review in Saturday's 3-0 loss to the Lightning.
Kulak scored the game-winning goal while shorthanded in Saturday's 3-0 win over the Avalanche.
Kulak scored a goal on three shots along with two hits and three blocked shots in Saturday's loss to the Lightning.
Kulak was a healthy scratch for Wednesday's 2-1 loss to the Avalanche.
Kulak will remain part of the starting six defensemen, Stu Cowan of the Montreal Gazette reports.
Kulak had two shots, a hit and a takeaway over 19:14 of ice time on the second pair in Friday's 3-2 loss to Buffalo.
Kulak was recalled from AHL Laval on Thursday and will join the team in Buffalo ahead of Friday's game versus the Sabres.
Kulak was brought in via trade from Calgary on Wednesday in exchange for Matt Taormina (undisclosed) and Rinat Valiev.
Kulak was placed on waivers by Calgary on Sunday, Wes Gilbertson of the Calgary Sun reports.