Weinstein, 74, is expected to remain behind bars due to his convictions in other cases.
Weinstein was a top film producer until sexual misconduct allegations led to his downfall and fuelled a wider social movement that encouraged women to come forward with accounts of sexual abuse by powerful men.
His most recent trial centred on Mann's allegation that Weinstein raped her in a Manhattan hotel room in 2013 while Mann resisted and repeatedly said "No".
It was not immediately clear whether prosecutors would seek to try the case for a fourth time.
Manhattan District Attorney Alvin Bragg, whose office brought the case, said his office was disappointed but respected the jury system.
"We will consider our next steps in consultation with Ms Mann," Bragg said in a statement.
Weinstein had pleaded not guilty to one count of third-degree rape and has denied assaulting anyone or having non-consensual sex.
His lawyers have argued that Mann fabricated the rape allegation after regretting that her consensual romance with Weinstein failed to advance her film career.
At his first trial in New York in 2020, Weinstein was convicted of raping Mann and assaulting onetime production assistant Miriam Haley in 2006.
But the state's highest court overturned the conviction and Weinstein's 23-year prison sentence after concluding he did not get a fair trial.
A Manhattan jury then convicted Weinstein of sexually abusing Haley at a trial in June 2025 but found him not guilty of assaulting former model Kaja Sokola.
The jury deadlocked on the third-degree rape charge accusing Weinstein of assaulting Mann, leading Justice Curtis Farber to declare a mistrial on that count.
The retrial began in April.
During their third day of deliberations on Friday, jurors sent Farber a note saying they were deadlocked.
The judge urged them to keep trying to reach a verdict.
Farber said outside the presence of the jury that it was clear they were "hopelessly deadlocked" and that there was no reason to keep them any longer.
He told lawyers for both sides to return for a hearing on June 25.
Weinstein was also convicted of rape in California in 2022 and is serving a 16-year prison sentence.
He is appealing that conviction and sentence.
The Miramax studio co-founder will face up to 25 years in prison when he is sentenced for abusing Haley.
