Ms Carroll, 75, said the incident took place in 1995 or 1996 after she came across Mr Trump while they were shopping.
According to Ms Carroll, Mr Trump asked her for advice on buying lingerie for an unnamed woman.
She said they both suggested they should each try on the item of lingerie.
However, she said: “The moment the dressing-room door is closed, he lunges at me, pushes me against the wall, hitting my head quite badly, and puts his mouth against my lips.”
She accused Mr Trump of pinning her against the wall and pulling down her tights, at which point he unzipped his trousers and raped her.
She said Mr Trump remained fully dressed throughout the attack and she finally managed to push him off her and escape the dressing room.
At the time Mr Trump, who was around 50 years old, was married to Marla Maples.
Ms Carroll said she confided in two friends at the time and one of them told her to report the incident to the police.
But another friend advised her against it, saying: "Forget it! He has 200 lawyers. He'll bury you."
Ms Carroll said she never went to the police because she was afraid of “receiving death threats, being driven from my home, being dismissed, being dragged through the mud”.
She added: “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, never sounded like much fun.”
The US president flatly denied her allegation and claimed to have “never met this person in my life”.
He accused her “trying to sell a new book - that should indicate her motivation. It should be sold in the fiction section."
The New York magazine article in which Ms Carroll made her revelation included an image of her and Mr Trump together at an NBC party around 1987.
When asked about the photo on Saturday, Mr Trump said: "Standing with my coat on in a line, give me a break, with my back to the camera. I have no idea who she is.
"There is some picture where we're shaking hands it looks like at some kind of event. I have my coat on, I have my wife standing next to me, and I didn't know her husband but he was a newscaster. But I have no idea who she is."
