In a late-night spray on social media platform Truth Social, Mr Trump slammed Mr Turnbull on Monday afternoon (AEDT).
"Malcolm Turnbull, the former Prime Minister of Australia who was always leading that wonderful country from "behind," never understood what was going on in China, nor did he have the capacity to do so," the president wrote.
"I always thought he was a weak and ineffective leader and, obviously, Australian's agreed with me!!!"
Mr Turnbull lost the prime ministership in a party leadership spill and was not voted out by the public.
Mr Turnbull has been contacted for comment.
He had earlier publicly said the US president was unpredictable and could not be trusted to take military action if Australia was attacked.
Mr Trump has not said whether he will exempt Australia from the tariffs, with a decision expected within days.
Prime Minister Anthony Albanese said his government would continue to engage "constructively" with the Trump administration.
"We are partners with the United States through our free trade agreement, and we'll continue to advocate for Australia's national interest," he told reporters in Lismore ahead of the social media post.
Australia is arguing it should be handed an exemption because it imports more from the US than what it exports, the same successful argument Mr Turnbull used when he was prime minister during Mr Trump's first term.
The US president's top economic advisor Kevin Hassett has said he doubted any exceptions would be made.
