The news comes 10 days after Weinstein was found guilty of sexual assault and third-degree rape in his New York City criminal trial.
Weinstein was in the process of being moved early on Thursday afternoon, his spokesman Juda Engelmayer told Reuters.
On Wednesday, Weinstein underwent a procedure to remove a heart blockage, Engelmayer said.
Weinstein was taken to Manhattan’s Bellevue hospital following his conviction on 24 February.
On Wednesday, he underwent a procedure to remove a heart blockage, Engelmayer said. He was suffering from chest pains and high blood pressure, his lawyer said at the time.
Weinstein is expected to be held at Rikers’ North Infirmary Command section, which houses inmates requiring medical care.
The Rikers Island jail complex, whose main building went up in 1932, has long been plagued by violence and neglect. New York City Mayor Bill de Blasio vowed in 2017 to close it within a decade.
Weinstein faces up to 29 years in prison. He’s scheduled for sentencing on 11 March.
Additional reporting by agencies