The upcoming drama from Cruise's Magnolia director Paul Thomas Anderson centres on the charismatic leader of a faith-based organisation, a character widely believed to be based on Scientology founder L Ron Hubbard.
It was previously reported that Anderson had screened the film for Cruise, who "had issues" with its content, and the New York Daily News now reports that Church of Scientology officials are angry about the film's implications.
Specifically, they reportedly object to one scene in which Hoffman's character is said to be "making [the religion] up as he goes along", taking this as a slight against Hubbard.
Philip Seymour Hoffman plays the leader, with Joaquin Phoenix starring as the aimless young man who becomes his second-in-command.
Spokespeople for Cruise declined to comment, while Scientology spokeswoman Karin Pouw said: "No-one in the church has seen the film, and we have no comment."
It was reported that Cruise was trying to put a stop to the film while it was still in pre-production.
The Master hits cinemas in the US on October 12, and comes to the UK on November 9. Watch a trailer below: