Weinstein, once one of the most powerful figures in Hollywood, is facing a retrial after a state appeals court last year overturned his 2020 conviction.
He was accused by prosecutors in the case of raping an aspiring actress and assaulting two other women.
Weinstein, 73, pleaded not guilty and has denied assaulting anyone or having non-consensual sex.
The jury found Weinstein guilty on one of the three counts he faced, which stemmed from his alleged assault of former production assistant Miriam Haley in 2006.
The jury found Weinstein not guilty of a charge stemming from his alleged assault of Kaja Sokola in 2002 when she was a 16-year-old aspiring actress.
The jury has not yet reached a verdict on the third count, which charges him with raping aspiring actress Jessica Mann in 2013.
They will resume deliberations on that count on Thursday.
Regardless of their eventual verdict on the rape charge, Weinstein faces up to 25 years in prison when he is sentenced.
He has separately been sentenced to 16 years in prison following a rape conviction in California.
Jurors in the New York case reached their partial verdict on the fifth day of sometimes fractious deliberations.
Before the jury announced their verdict on Wednesday, Justice Curtis Farber met privately with one person on the 12-member jury referred to as Juror One.
The judge then stated in open court that there had been "fighting" in the jury room.
"Juror One has made it very clear that he is not going to change his position," Farber said, adding that Juror One did not tell him what his position was.
"He indicated that at least one other juror made comments to the juror that 'I'll meet you outside one day,' and there's yelling and screaming."
Weinstein's lawyer Arthur Aidala asked for a mistrial.
As Farber was preparing to dismiss jurors for the day to give them a chance to "cool off," the jury sent a note indicating it had reached a verdict on some counts.
The retrial began on April 23. Weinstein has had a litany of health problems and attended the retrial in a wheelchair.
In closing arguments on June 3, the prosecution told the 12 jurors that the evidence showed how Weinstein used his power and influence to trap and abuse women.
The defence countered that the accusers lied on the witness stand out of spite after their consensual sexual encounters with the Oscar-winning producer failed to result in Hollywood stardom.
A jury had in February 2020 found Weinstein guilty of raping Mann and sexually assaulting Haley.
Sokola's allegation was not part of that case.
The conviction was a milestone for the MeToo movement, which encouraged women to come forward with allegations of sexual misconduct by powerful men.
But the New York Court of Appeals, the state's highest court, threw out that conviction in April 2024.
It said the trial judge erred by letting women testify that Weinstein had assaulted them, although their accusations were not the basis of the criminal charges.
Although the 2020 conviction was thrown out, Weinstein has remained behind bars because of his 2022 rape conviction in California, which resulted in a 16-year prison sentence.
He is appealing that verdict.
More than 100 women, including famous actresses, have accused Weinstein of misconduct.
The retrial was handled by prosecutors with the office of Manhattan District Attorney Alvin Bragg.
They portrayed Weinstein as a serial predator who promised career advancement in Hollywood to women, only to then coax them into private settings where he attacked them.
The defence rejected that characterisation, saying Weinstein engaged in "mutually beneficial" relationships with his accusers, who ended up with auditions and other show business opportunities.
Weinstein co-founded the Miramax studio, whose hit movies included Shakespeare in Love and Pulp Fiction.
His own eponymous film studio filed for bankruptcy in March 2018, five months after sexual misconduct accusations against him became widely publicised.
