Appearing in court while wearing a GPS 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.
Lawyers representing the 66-year-old, a father of five, claim the development taints the entire case against him.
Predicting the judge may throw out all of the allegations, Weinstein’s lawyer Ben Brafman told reporters: “”This is obviously a very positive development.”
In a story published by The New Yorker magazine a year ago, Ms Evans alleged the assault happened during a meeting in his office when she was a 21-year-old student.
Ms Evans’ lawyer, Carrie Goldberg, claimed that the prosecutors’ decision not to oppose the dismissal of the charge had seen them “abandon” her client.
She said: “Let me be clear: the decision to throw away my client’s sexual assault charges says nothing about Weinstein’s guilt or innocence.
“Nor does it reflect on Lucia’s consistent allegation that she was sexually assaulted with force by Harvey Weinstein.
“It only speaks volumes about the Manhattan district attorney’s office and its mishandling of my client’s case.”
Mr Brafman told the judge that Ms Evans had lied to both a grand jury and to The New Yorker about her encounter with Weinstein.
He also claimed a police officer had corruptly attempted to influence the case by keeping a witness from testifying about her misstatements.
“The integrity of these proceedings has been compromised,” Mr Brafman said.
Weinstein’s defence lawyer later suggested, outside court, that Ms Evans should be criminally prosecuted for perjury.
He added: “The case against Mr Weinstein is, in my view, not sustainable. I’m not certain he [the judge] will have any choice but to dismiss the entire indictment against Harvey Weinstein.”
Details of the potential problems with Ms Evans’ testimony were not discussed in court, but were expected to be included in court filings set to be unsealed on Thursday.
Five remaining charges in the criminal case include claims Weinstein raped a woman in 2013 and forced a sex act on a different woman in 2006.
Weinstein denies assaulting anyone.
Assistant district attorney Joan Illuzzi-Orbon said the rest of the prosecution’s case was strong, telling the judge: “In short, your honour, we are moving full steam ahead.”
The revelation of numerous allegations about Weinstein, beyond the three women involved in the criminal case, helped spark the #MeToo movement against sexual harassment and sexual assault.