Asked if she thinks the president "has a grasp of economic policy," Yellen flatly responded, "No, I do not."
"Well, I doubt that he would even be able to say that the Fed's goals are maximum employment and price stability, which is the goals that Congress have assigned to the Fed," she added in the interview with American Public Media's "Marketplace." "He's made comments about the Fed having an exchange-rate objective in order to support his trade plans, or possibly targeting the U.S. balance of trade. And, you know, I think comments like that shows a lack of understanding of the impact of the Fed on the economy, and appropriate policy goals."
The comments mark a departure for Yellen, who has mostly handled her issues with Trump by not saying much of anything.
When he campaigned for president in 2016, Trump said Yellen should be "ashamed" of her handling of monetary policy, accusing her of keeping interest rates artificially low to boost the fortunes of former president Barack Obama, who appointed Yellen as chair.
Though Trump softened his tone somewhat after he took office, he decided against reappointing her, making her the first Fed chair not to get a second four-year term since the Jimmy Carter administration.
Yellen had little to say, though, about not getting the reappointment, and went on to join her predecessor, Ben Bernanke, as a fellow at the Brookings Institution. She also is incoming president of the American Economic Association.
When it comes to economics, she said Monday that Trump misunderstands some fairly elementary concepts, citing his stance on reducing trade deficits with China and other global partners.
"And when I continually hear focus by the president and some of his advisers on remedying bilateral trade deficits with other trade partners, I think almost any economist would tell you that there's no real meaning to bilateral trade deficits, and it's not an appropriate objective of policy," she said.
Yellen is not alone in getting skewered by Trump.
Her successor, Jerome Powell, has come under intense criticism for raising interest rates, and there was even speculation that Trump might replace him.
Yellen said Trump's pressure on what is supposed to be an independent Fed isn't healthy.
"President Trump's comments about Chair Powell and about the Fed do concern me, because if that becomes concerted, I think it does have the impact, especially if conditions in the U.S. for any reason were to deteriorate, it could undermine confidence in the Fed," she said. "And I think that that would be a bad thing."
Read the full interview here.