A description of the alleged attack was excerpted by New York magazine in an article published Friday.
The White House did not return CNBC's request for comment, but strongly denied Carroll's claims to New York. A senior White House official told the magazine, "This is a completely false and unrealistic story surfacing 25 years after allegedly taking place and was created simply to make the President look bad."
Trump issued a statement later Friday saying he had "never met this person" and claiming the account was an attempt "to get publicity" and "sell a book."
The alleged attack occurred "in the fall of 1995 or the spring of 1996," according to Carroll. At the time, Trump was married to his second wife, Marla Maples.
"I try to push him off with my one free hand — for some reason, I keep holding my purse with the other — and I finally get a knee up high enough to push him out and off and I turn, open the door, and run out of the dressing room," Carroll writes.
The article is entitled: "Hideous Men: Donald Trump assaulted me in a Bergdorf Goodman dressing room 23 years ago. But he's not alone on the list of awful men in my life."
The article details several other alleged sexual assaults and unwanted advances that Carroll says she has suffered since she was a child.
It includes an account of former CBS CEO Les Moonves, after an interview with Carroll, aggressively groping her in an elevator before she is able to get away from him. Moonves stepped down from the media giant in September after several women accused him of sexual misconduct, which he denied.
Moonves "emphatically denies" Carroll's claims, according to New York magazine.
The publication noted that Caroll, 75, is at least the 16th woman to accuse Trump of sexual misconduct. Her forthcoming book is entitled "What Do We Need Men For? A Modest Proposal."
"I'm automatically attracted to beautiful women — I just start kissing them, it's like a magnet. Just kiss. I don't even wait. And when you're a star, they let you do it. You can do anything," Trump said on the recording. "Grab 'em by the pussy."
Carroll wrote that she never reported the incident with Trump to the police, despite one of the two friends at the time begging her to go to law enforcement.
Both friends confirmed to New York magazine that they still remember her telling them about Trump's actions, the publication reported.
Carroll wrote that she had never before gone public with her account of Trump because "I am a coward," and because she wanted to avoid death threats, "being driven from my home, being dismissed, being dragged through the mud, and joining the 15 women who've come forward with credible stories about how the man grabbed, badgered, belittled, mauled, molested, and assaulted them, only to see the man turn it around, deny, threaten, and attack them."
Carroll, who authorized a biography of gonzo journalist Hunter S. Thompson, and is currently an advice columnist at Elle magazine, wrote she ran into Trump one day when she was leaving Bergdorf's and he recognized her, saying, "Hey, you're that advice lady!"
She responded, "Hey, you're that real-estate tycoon!."
She writes that Trump said, "Come advise me ... I gotta buy a present," for another woman.
Carroll said Trump asked her opinion about several items in the upscale store on Fifth Avenue in Manhattan, across the street from Trump Tower, before asking her to try on a "lacy see-through bodysuit of lilac gray."
After she laughed him off, suggesting that Trump try on the bodysuit, he took her arm and said, "Come one. ... Let's put this on," she wrote.
Carroll wrote that she was "staggered by my stupidity" in allowing herself to go to a dressing room with Trump.
"As we head to the dressing rooms, I'm laughing aloud and saying in my mind: I'm gonna make him put this thing on over his pants!" Carroll wrote.
She wrote that Trump "lunges at me" the moment the dressing room door closes, pushed her against the wall, and putting his mouth on her.
"I am so shocked I shove him back and start laughing again," Carroll wrote.
"He seizes both my arms and pushes me up against the wall a second time, and, as I become aware of how large he is, he holds me against the wall with his shoulder and jams his hand under my coat dress and pulls down my tights."
"I am astonished by what I'm about to write: I keep laughing. The next moment, still wearing correct business attire, shirt, tie, suit jacket, overcoat, he opens the overcoat, unzips his pants, and, forcing his fingers around my private area, thrusts his penis halfway — or completely, I'm not certain — inside me," she wrote.
She said the entire episode in the dressing room lasted no longer than three minutes.
Carroll wrote that the Donna Karan coat-dress that she was wearing during the alleged assault has remained in her closet, "unworn and unlaundered since that evening."
"I have never had sex with anybody again," she wrote.
Carroll wrote that when she told two close friends about the alleged attack, one of them, a journalist, urged her to contact police.
Carroll wrote: "'He raped you,' she kept repeating when I called her. 'He raped you. Go to the police! I'll go with you. We'll go together.'"
But the other friend, who is a New York anchorwoman, "grew very quiet when I told her."
"Tell no one. Forget it! He has 200 lawyers. He'll bury you," that woman told Carroll, according to the article.