Anderson's first film since 2007's There Will Be Blood stars Philip Seymour Hoffman as the charismatic leader of a 1950s faith-based organisation called "the Cause".
Many have compared the organisation to Scientology, and suggested that Hoffman's character is modelled on L Ron Hubbard.
Joaquin Phoenix, who features prominently in the trailer, co-stars as the right hand man who begins to question his mentor and the organisation's belief system.
The cast also includes Amy Adams, Laura Dern and Jesse Plemons.
It was rumoured last year that Tom Cruise was attempting to halt production on the film on the grounds that it could reveal "secrets" of Scientology, but this was denied by Cruise's reps.
The Master is due to be released on October 12 in the US, with a UK date yet to be set.