The women's allegations against the 65-year-old movie mogul, according to the magazine, include unwanted oral sex and forced oral and full sex.
Weinstein denies all charges, according to a statement from his spokeswoman Sallie Hofmeister, circulated among US media.
The accusations will be seen as a hugely damaging escalation of the scandal engulfing the Oscar-winning producer, as the numerous allegations which led to his weekend sacking from The Weinstein Company had so far been limited to complaints about harassment.
Italian director and actress Asia Argento poses during the photocall for 'Incompresa' (Misunderstood) at the 67th annual Cannes Film Festival, in Cannes. Source: AAP
The investigation was published as fresh misconduct allegations emerged from Hollywood A-listers such as Angelina Jolie, Rosanna Arquette and Gwyneth Paltrow.
Argento, the 42-year-old daughter of iconic horror director Dario Argento, said Weinstein forced oral sex on her 20 years ago.
She told the publication she had maintained her silence until now for fear that Weinstein would "crush" her, adding: "I know he has crushed a lot of people before."
She said Weinstein, who has weighed up to 300 pounds (136 kilograms), terrified her due to his immense size.
"It wouldn't stop. It was a nightmare," she added, revealing that she had felt forced to pretend she was enjoying the attack in hopes that it would be over with sooner.
Lucia Evans, an aspiring actress, said she met Weinstein at the Miramax office in New York in 2004 and that he forced her to perform oral sex on him.
"I said, over and over, 'I don't want to do this, stop, don't,'" she told the New Yorker.
"I tried to get away, but maybe I didn't try hard enough. I didn't want to kick him or fight him."
'People give up'
Evans said she was overpowered and "just sort of gave up."
"That's the most horrible part of it, and that's why he's been able to do this for so long to so many women: people give up, and then they feel like it's their fault," she added.
Another woman, who was too afraid to allow her name to be published, told the New Yorker Weinstein brought her to a hotel room for a meeting.
He changed into a bathrobe, she said, and "forced himself on me sexually."
She felt "horror, disbelief, and shame," and thought about going to the police, but decided it would be a case of "he said, she said," and worried about how powerful his legal team would be, and how much she had to lose.
A media report says Harvey Weinstein raped three women, something the media mogul denies. (AAP) Source: AAP
Another instance involved model Ambra Battilana Gutierrez, once a finalist in the Miss Italy contest, whom the New Yorker said Weinstein met in March 2015 at a reception for a show he was producing in New York.
According to the New Yorker, Gutierrez says Weinstein "lunged at her, groping her breasts and attempting to put a hand up her skirt" at a meeting in his offices in Tribeca.
She reported the incident and the New York Police Department asked her to wear a wire to his play "Finding Neverland."
Audio of their conversation in the hallway of his room at the Tribeca Grand Hotel was released by the magazine.
In the tape, Gutierrez is heard asking Weinstein: "Why yesterday you touch my breast?"
"Oh, please, I'm sorry, just come on in, I'm used to that. Come in, please," he replies.
"You're used to that?" she asks, to which he again asks her to come into his room.
She refuses, and Weinstein pleads: "I won't do it again, come on, sit here. Sit here for a minute, please?"
Authorities decided not to press charges, according to the New Yorker, after it emerged the young woman had attended one former Italian prime minister Silvio Berlusconi's infamous "bunga bunga" sex parties and, as a teenager, had made a sexual assault allegation and then declined to cooperate with prosecutors.
Weinstein was fired late Sunday from his own film studio, three days after a bombshell New York Times report alleged that the Oscar-winning producer behind such hits as "The King's Speech" and "The Artist" had preyed on young women hoping to break into the industry.
His accusers said he had promised to help advance their careers in exchange for sexual favors, pressuring them to massage him and watch him naked.
The Times, as well as various entertainment media, separately reported on Tuesday that the litany of Weinstein's harassment victims also included Gwyneth Paltrow, who was 22 when the magnate hired her for the lead in the Jane Austen adaptation "Emma."
Hollywood A-lister Angelina Jolie, "Pulp Fiction" star Rosanna Arquette and French actress Judith Godreche, all say they too were victims of his unwanted advances, the Times reported.
In this June 5, 2017 file photo, former Secretary of State Hillary Clinton speaks in Baltimore. Clinton says she's "shocked and appalled" by the revelations. Source: AAP
Clinton 'shocked and appalled'
"I was shocked and appalled by the revelations about Harvey Weinstein," former Democratic presidential hopeful Hillary Clinton said in a statement Tuesday.
"The behavior described by women coming forward can not be tolerated," she added. "Their courage and the support of others is critical in helping to stop this kind of behavior."
Australian actress Nicole Kidman released a statement applauding women for speaking out against abuse and the misuse of power.
Kidman has previously collaborated with Weinstein, with some of her most successful films - including award nominated roles in Lion and Cold Mountain, and bomb Grace of Monaco - made with him.
"As I've stated before publicly, I support and applaud all women and these women who speak out against any abuse and misuse of power - be it domestic violence or sexual harassment in the workforce," Kidman, in a statement released to People magazine, said.
"We need to eradicate this behaviour."
Kidman has been a vocal crusader for women.
