The storyline, which sees liberals hunt Trump supporters, has been criticised by the president.
The Hunt, a satirical film in which liberals hunt Trump supporters and kill them for sport, was due to be released on 27 September.
Marketing of the film had already been put on hold following the El Paso and Dayton shootings.
Universal said the decision was made after "thoughtful consideration."
The Hunt's storyline is intended to reflect the divided nature of US politics.