Schwarzenegger had announced on Friday that he would not return for a second season of the NBC show. He blamed Trump, an executive producer and former host of the show, for low ratings, describing the president's involvement as "baggage."
Trump sees it differently.
Arnold Schwarzenegger isn't voluntarily leaving the Apprentice, he was fired by his bad (pathetic) ratings, not by me. Sad end to great show— Donald J. Trump (@realDonaldTrump) March 4, 2017
The squabble then continued on Twitter.
"You should think about hiring a new joke writer and a fact checker," a message on Schwarzenegger's Twitter account read, responding to Trump.
NBC, a unit of Comcast Corp on Friday, did not comment on Schwarzenegger's decision not to return for another season, or on the show's future.
Schwarzenegger, a movie star and former California governor, took over as host of "Celebrity Apprentice" last year. His first season premiered in January, and was watched by around 4 million to 5 million viewers.
Schwarzenegger, a Republican who served two terms as California governor but said he did not vote for Trump as president, told British film magazine Empire in an interview published on Friday that he was leaving the show due to Trump's involvement.
News that Trump will retain an executive producer credit on the show, which usually involves a payment, caused a media furor in December about potential conflicts of interest.
Schwarzenegger told Empire that the show was "a really great opportunity, but "under the circumstances I don't want to do it again."
"When people found out that Trump was still involved as executive producer and was still receiving money from the show, then half the people (started) boycotting it," Schwarzenegger said.
Trump was a celebrity businessman long before he became president, and hosted "The Apprentice" and "The Celebrity Apprentice" for 14 seasons, overseeing contestants competing in business challenges before deciding which ones to fire.