U.S. District Judge Lewis Kaplan canceled testimony on Monday after one juror who felt ill was sent home for a COVID test, and Trump's lawyer Alina Habba said she caught a fever after dining with her parents, one of whom contracted the virus.
Tuesday's trial session was later also canceled, a court officer said.
The trial concerns Trump's June 2019 denials of Carroll's claim that he raped the former Elle magazine advice columnist in the mid-1990s in a Bergdorf Goodman department store dressing room in Manhattan.
A different jury last May ordered Trump to pay Carroll $5 million over a similar October 2022 denial.
Kaplan has ruled that the first trial established that Trump defamed and sexually abused Carroll.
The only issue for the nine jurors in the second trial is how much money Trump should pay Carroll, if any. Carroll, 80, is seeking at least $10 million.
Prior to the postponement, Habba said Trump "had been planning to testify" after Carroll's lawyers finished presenting their case.
Trump plans to be in New Hampshire on Tuesday for that state's Republican presidential primary, where he has been leading in opinion polls.
The winner of the nomination is expected to face President Joe Biden, the likely Democratic nominee, in November.
Carroll's lawyer Roberta Kaplan, who is not related to the judge, said she had a "very short" amount of testimony left to present.
Habba and her co-counsel, Michael Madaio, tested negative for COVID-19 on Monday. Neither they nor Trump wore masks in the courtroom.
NO MISTRIAL
Trump, 77, has consistently denied wrongdoing, and accused Carroll of making up their encounter to boost sales of her then-new memoir.
In a post on his Truth Social website following Monday's postponement, Trump maintained that he knows "absolutely nothing about" Carroll, and that the case was "one of the many Crooked Joe Biden-inspired Witch Hunt trials."
Trump has also pleaded not guilty in four criminal cases, including two claiming he tried illegally to overturn his 2020 loss to Biden.
Judge Kaplan separately denied Trump's request for a mistrial, which arose from Carroll testifying that she destroyed emailed death threats after first accusing Trump of rape.
Trump did not attend Carroll's first trial, and attended jury selection and the first full day of her second trial.
He is not required to testify, and Carroll's lawyers have argued he might try to "sow chaos" if he did, perhaps believing that doing so would help him politically.
Last Wednesday, Judge Kaplan warned Trump he might be ejected for being disruptive in the courtroom, after a lawyer for Carroll said jurors might have overheard Trump loudly proclaim the trial a witch hunt and "con job."
"I would love it," Trump said.
"I know you would," Kaplan replied.
