"Trump's visa ban for Iranians is racist. Whether this will include a cultural event or not, I won't attend the #AcademyAwards 2017 in protest," tweeted Taraneh Alidoosti, the film's 33-year-old lead actress.
Trump is reportedly poised to stop visas for travellers from seven Muslim countries, including Iran, for 30 days.
He told ABC News yesterday that his plan was not a "Muslim ban", but targeted countries that "have tremendous terror."
"The Salesman", directed by acclaimed Iranian filmmaker Asghar Farhadi is nominated for best foreign language film at the Academy Awards, which take place next month.