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.
The 66-year-old former movie mogul, who has denied all allegations of non-consensual sex, still faces charges over allegations that he raped an unidentified woman in his hotel room in 2013 and performed a forcible sex act on a different woman in 2006.
Assistant District Attorney Joan Illuzzi-Orbon told the judge that prosecutors wouldn't oppose dismissal of the count in the case involving Evans. The prosecution assured they are "moving full-steam ahead" on all other counts.
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.
The count stems from charges brought forth against the disgraced movie producer in May and July by the Manhattan District Attorney's Office. Rather, "it only speaks volumes about the Manhattan D.A.'s office and its mishandling of my client's case".
An attorney for the Harvey Weinstein accuser whose case has been dropped says it does not "invalidate the truth of her claims".
The witness told prosecutors that she and Evans met Weinstein in a bar during summer 2004.
The friend told prosecutors that Evans admitted she performed the sex act and during the conversation was "upset, embarrassed and shaking".
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The hearing comes a year and a day after The New Yorker first published allegations by one accuser in the case, Lucia Evans.
Brafman said the written account from Evans was discovered from a fact-checker at The New Yorker, and that he would subpoena the magazine.
Actress Lucia Evans alleges that Weinstein forced her to perform oral sex in 2004.
"The integrity of these proceedings has been compromised", Mr Brafman said. "If you have a person willing to commit perjury in the grand jury, that is as serious as the crime of sexual assault because it undermines the fairness of the process for all of us".
The development was announced in court with Weinstein looking on.
"We take these allegations seriously", Chief of Detectives Dermot Shea said. A message left on a phone used by the detective in the past wasn't immediately returned.
Brafman asserted again that Weinstein has not committed any crime and said he planned to file an application with the New York Police Department asking the detective who interviewed Evans to be banned from the case.
The numerous sexual misconduct accusations made against Weinstein, namely those made out of court, had raised awareness of the #MeToo movement and increased public debate about the issue of consent.