Weinstein appeared before New York Judge James Burke as his lawyers tried to have some or all of the charges he faces dismissed.
Appearing in court while wearing a Global Positioning System monitor and out on a $1m (£757,000) bail, the judge agreed to throw out the charge relating to Lucia Evans, who has accused Weinstein of forcing her to perform oral sex in 2004.
Prosecutor Joan Illuzzi-Orbon did not oppose the dismissal but added that this disclosure does not impact the strength of the remaining case. She insisted the rest of the case, involving two other accusers, was strong.
"In short, your honor, we are moving full steam ahead", she said.
Weinstein's lawyer, Benjamin Brafman, told the judge he believed Evans lied to the grand jury. The union representing New York City police detectives also didn't return a message.
"When one of the principal allegations in this indictment is predicated on perjured testimony that's a very big, important development", Brafman told reporters.
"Any assertion by lawyers for Harvey Weinstein that The New Yorker had information that contradicted Lucia Evans's account is patently incorrect".
Some media outlets reported that there were problems with witness interviews done by one of the lead police detectives handling the investigation.
An attorney for the Harvey Weinstein accuser whose case has been dropped says it does not "invalidate the truth of her claims".
Ms Evans's lawyer, Carrie Goldberg, said her client's account of events had been accurate.
While more than 75 women have publicly accused Weinstein of sexual misconduct over the past year, the criminal case in New York City involves the allegations of just three women: Evans, an unidentified woman who says he raped her in a hotel room in 2013, and an actress who said Weinstein performed a forcible sex act on her in 2006.
"We know of no evidence refuting our client's report that Harvey Weinstein forcefully sexually assaulted her", she said in a statement. Rather, "it only speaks volumes about the Manhattan D.A.'s office and its mishandling of my client's case".
The woman who accused Weinstein of assaulting her in 2004, Lucia Evans, told the New Yorker in October 2017 that Weinstein forced her to perform oral sex on him when she was a 21-year-old college student. Weinstein, 66, has pleaded not guilty and is free on $1 million bail.
The collapse of part of the case against him could mean trouble for the prosecutor.
Evans told her friend when they walked home that night that she had flashed her breasts to Weinstein in the restaurant's hallway. At the time, Vance cited a lack of supporting evidence, despite the existence of a clandestinely made recording of Weinstein discussing the episode with the woman.
In another blow to the case, prosecutors obtained a 2015 draft email that Evans wrote to her husband, who was then her fiancé, in which she recounted the encounter with Weinstein.
New York Police officials poured on the pressure, too, saying publicly they believed they had gathered ample evidence to make an arrest.