Sony Pictures reversed course Tuesday and said it would release “The Interview” on Christmas Day, though only a small number of theaters signed on to show the controversial farce amid fears of reprisals from a group of hackers and frustration with the studio’s quick-changing distribution strategy.

The studio’s decision to release the film—and to try to distribute it via video-on-demand—came just six days after the Sony Corp. unit said it was canceling the film’s release, following a devastating cyberattack that the U.S. blames...