In an interview with far-right British political operative Nigel Farage on London's GB News channel, the second-time presidential hopeful responded to years-old comments made by Mr Rudd.
Prior to his appointment as US ambassador, Australia's 26th prime minister was a vocal critic of the Republican president, calling Mr Trump a "traitor to the west" and "the most destructive president in history" who "drags America and democracy through the mud".
Donald Trump has questioned Kevin Rudd's intelligence. (AP PHOTO)
Mr Trump has now returned fire, issuing a warning to Mr Rudd.
"I don't know much about him, I heard he was a little bit nasty," he told Mr Farage.
"I hear he's not the brightest bulb ... if he's at all hostile, he will not be there long."
The US presidential election in November is a rematch between Democrat President Joe Biden and Mr Trump.
Mr Biden's approval rating has continued to slip, while the former president is contending with multiple criminal charges.
Nationals leader David Littleproud warns Mr Rudd's past comments could have consequences for Australia's alliances and defence deals if Mr Trump wins the election.
"We're going to have a very difficult time in negotiating with the new administration, particularly with things as important as AUKUS," he said on Sky.
Politicians should instead wait for the outcome of the election and avoid commenting on other country's domestic political situations, Deputy Opposition Leader Sussan Ley said .
"I'm not going to make commentary on what might transpire ... I think people in this government now might be wondering why they made the comments they did at the time," she told Sky News.
"Kevin Rudd is our ambassador, we do want him to succeed because he represents the national interest."
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