He told prison staff he believed he had the virus when he entered the state prison system last week from Rikers Island, where several inmates have contracted the virus.
Weinstein is currently serving a 23-year sentence after being found guilty of two out of five charges of third-degree rape and sexual assault against two women.
He was seen using a walker to hobble into court most days and it was claimed that without daily medical injections he would lose his eyesight.
He was in custody at notorious Rikers Island until his sentencing on March 11 in New York State Supreme Court, where he was sentenced to 23 years in prison.
Weinstein has maintained that any sexual contact with his accusers was consensual. Countless allegations against Weinstein gave rise to the #MeToo movement in October 2017.
Over 80 women have accused him of sexual misconduct occurring over the past few decades.