On October 1, 2018, the Flames traded Kulak to the Montreal Canadiens in exchange for Matt Taormina and Rinat Valiev. Kulak was subsequently assigned to the Canadiens' AHL affiliate, the Laval Rocket.[7] On November 22, he was called up by the Canadiens after an injury to defenseman Noah Juulsen. He was immediately put into the line-up.