Karena Virginia said Mr Trump approached her when she was waiting for a car outside the US Open tennis tournament in New York in 1998.
She accused the current Republican nominee of grabbing her breast and making objectifying statements about her to other men in his group.
Mr Trump's campaign dismissed the claim as a "fictional story".
"Discredited political operative Gloria Allred, in another coordinated, publicity seeking attack with the Clinton campaign, will stop at nothing to smear Mr. Trump. Give me a break," said Jessica Ditto, a Trump campaign spokeswoman.
"Voters are tired of these circus-like antics and reject these fictional stories and the clear efforts to benefit Hillary Clinton."
Mrs Virginia - a yoga teacher who comes from the New York area - said she expected to be personally attacked by Mr Trump, but felt it was her "duty as a woman, as a mother, a human being, and as an American citizen to speak out and tell the truth about what happened to me".
"Perhaps he will label me just another nasty woman", Mrs Virginia added.
Mr Trump, at the final televised presidential debate in Las Vegas, called his Democratic opponent Hillary Clinton "such a nasty woman".
Speaking at a press conference in Los Angeles alongside her lawyer Gloria Allred, Mrs Virginia recounted her alleged encounter with Mr Trump when she was 27 years old.
She said she was waiting for her hire car to arrive when Mr Trump approached her and made comments about her physical appearance to a group of men he was with.
"He said: 'Hey look at this one. We haven't seen her before,'" Mrs Virginia tearfully recounted, saying that his words described her "as though I was an object rather than a person".
"Then his hand touched the right inside of my breast. I was in shock. I flinched."
She told reporters that Mr Trump then said to her: "Don't you know who I am?"
"I felt intimidated and I felt powerless," she said, explaining that the incident left her feeling "ashamed" and that she blamed herself for many years.
Mrs Allred - who is a vocal supporter of Mrs Clinton - insisted that her legal office was not working in co-ordination with the Clinton campaign, and that Mrs Virginia had sought her help to announce the accusation.
She said that there were no corroborating witnesses to the incident, but that Mrs Virginia had recounted the story to friends soon after, and also later to her husband.

He was in his hotel room in London, where he is due to perform at the Lyric Theatre, when officers barged in.
Tweeting about his predicament he said hotel staff mistook him for a guest who had threatened staff with a knife.
He was handcuffed and led from the room shouting "but I'm in my kegs". Met Police said he was mistakenly detained.
Geordie comic Ramsey is touring the country with his show All Growed Up and provided a running commentary on Twitter of Sunday night's events.
"Well... The police have definitely just kicked my hotel door in and handcuffed me," the first tweet, sent at 00:47, said.
In a string of follow-up tweets he said: "Hotel staff ID'd me as someone who had been in the hotel earlier threatening staff with a knife. So when I checked in just now they called the police and sent them up to my room! I kept asking 'is this a joke?' When he said 'no come with us' police put the handcuffs on me and began to march me out of the room when I shouted 'but I'm in my kegs'.
"I love the idea that someone who was in earlier threatening staff with a knife, would then check in later for a kip!!", he tweeted.
On his way to breakfast he said he was taking precautions by wearing an anonymous black cap and black T-shirt, lest he be mistaken for "a murderer or something".
Ramsey - who is a panel show regular and has also starred in BBC sitcom Hebburn - tweeted that his ordeal might be discussed during his stand-up routine later.
A Met Police spokesman confirmed officers had initially been called to deal with a man who was threatening hotel staff with a knife in a racially aggravated attack.
Officers returned to the hotel after midnight when they mistakenly arrested and subsequently released Ramsey, the spokesman said.
A tenth woman has come forward to accuse US presidential candidate Donald Trump of sexual assault.
[NEXT_CONCEPT]
Comedian Chris Ramsey was arrested at midnight in his underpants - but has since said he sees the funny side of the case of mistaken identity.