A spokesperson told CBC News's Ioanna Roumeliotis the cinemas aren't sure whether the decision will be reversed.
The Cineplex website in Canada currently shows no showing dates for the film.
"After careful consideration of this unprecedented and complex situation, Cineplex Entertainment will postpone presentation of the Sony Pictures movie, The Interview," Par Marshall, Cineplex's VP of communications and investor relations, told CBC News.
"Cineplex takes seriously its commitment to the freedom of artistic expression, but we want to reassure our guests and staff that their safety and security is our No. 1 priority. We look forward to a time when this situation is resolved and those responsible are apprehended."
Variety reports that Regal Cinemas, Cinemark and AMC Entertainment have also dropped their premieres, which along with Cineplex represents four out of five of the top chains in the U.S.
The fallout from the Sony Pictures Entertainment hack that began four weeks ago exploded Tuesday after the shadowy group calling themselves Guardians of Peace escalated their attack beyond corporate espionage and threatened moviegoers with violence reminiscent of the terrorist attacks of Sept. 11, 2001.