The president taunted Schwarzenegger for the show's recent poor performance in the ratings, even mocking him during an address at the National Prayer Breakfast.
In an interview with Empire Magazine, Schwarzenegger confirmed rumours that he is to exit the show at the end of this season - and cited Donald Trump himself as the reason why the show is failing. He also said that now is a very divisive period and he thought that the show got caught up in all the division, as stated in Orange County Register.
"Yes, Arnold Schwarzenegger did a really bad job as Governor of California and even worse on the Apprentice...but at least he tried hard!", Trump wrote.
"You should think about hiring a new joke writer and a fact checker", Schwarzenegger said in response to Trump's tweet.
The Terminator star and Trump - who has remained an executive producer of the competition series - have exchanged barbs since the new season debuted in January.
In the video, Schwarzenegger said, "Hey, Donald, I have a great idea".
After weeks of harassment from Trump and bad press for the show's low quality (including a lazy catchphrase), Schwarzenegger has announced he's parting ways with the NBC reality show.
In a statement, Schwarzenegger said: "I loved every second of working with NBC and Mark Burnett". Schwarzenegger refused to support Trump during the campaign, and Trump has since lashed out at Schwarzenegger over "Apprentice" ratings.
Schwarzenegger quickly fired back at Trump.
In his tweet, Trump alleged that Schwarzenegger was sacked as the host of "The New Celebrity Apprentice" due to his poor ratings - contradicting what the latter said Friday in an interview with the Empire magazine. "So much for ... being a movie star-and that was season 1 compared to season 14", Trump had written.
The show, whose 15th season ended last month, averaged fewer than five million viewers per episode.
NBC had not responded to requests for comment at the time of publication.