On January 15, 2014, Edmonton traded Dubnyk to the Nashville Predators in exchange for forward Matt Hendricks. After starting in only two games as a Predator, Dubnyk was sent to the AHL's Milwaukee Admirals on March 3 to accommodate goaltender Pekka Rinne's return from long-term injured reserve. Two days later, on March 5, Dubnyk was again traded, this time to the Montreal Canadiens in exchange for future considerations from Nashville. He was then immediately assigned to Montreal's AHL affiliate, the Hamilton Bulldogs, failing to make an appearance for Montreal.