He was sentenced to 23 years behind bars but has been isolated after the outbreak at the Wende correctional facility in upstate New York.
Michael Powers, president of the New York State Correctional Officers and Police Benevolent Association, confirmed Weinstein had contracted the virus sweeping the globe.
An officer at the jail said two prisoners had tested positive on Sunday, while several members of staff have also been quarantined for their safety.
Weinstein was previously being held at Rikers Island, as well as spending time in hospital receiving treatment for chest pains.
He was convicted of first-degree criminal sexual act against production assistant Miriam Haley in 2006 and third-degree rape of aspiring actress Jessica Mann in 2013.
The Hollywood personality, whose crimes sparked the #MeToo movement, was acquitted of predatory sexual assault.
His lawyers plan to lodge an appeal against his conviction.
According to the BBC, Weinstein's legal team had not yet been aware of the coronavirus diagnosis.
Imran Ansari told the BBC: 'Given Mr Weinstein's state of health, we are of course concerned, if this is the case, and we are vigilantly monitoring the situation.'
It comes as governments all over the world implement strict measures in a bid to curb the spread of coronavirus.