The footage was filmed after Trump's first term as President, and shows former Prime Minister Rudd calling him a "village idiot" and "incoherent".
It was taken from a webinar Rudd did with Dr Shashi Tharoor, an Indian politician and former diplomat.
"The United States, in the past four years, has been run by a village idiot," Rudd said.
"People have seen China continuing to be competent in its national statecraft and the United States increasingly incompetent in its national statecraft under Trump."
It comes days after Rudd deleted a number of tweets that were critical of Trump following the Republican candidate's win in the Presidential election.
In 2020, Rudd - before he was appointed as Australia's ambassador to the US - called Trump "the most destructive president in history".
A statement from Rudd's office said the tweets had been deleted to "avoid them being misconstrued".
"In his previous role as the head of an independent US-based think tank, Mr Rudd was a regular commentator on American politics," the statement said.
"Out of respect for the office of president of the United States, and following the election of President Trump, Ambassador Rudd has now removed these past commentaries from his personal website and social media channels.