Thomas Mailey, a spokesman for the state prison system, declined to comment on Mr. Weinstein’s health, citing privacy rules regarding medical records.

In February, a jury of seven men and five women in Manhattan convicted Mr. Weinstein of rape and criminal sexual act, and earlier this month, a judge sentenced him to 23 years in prison, which his lawyers said would amount to a life sentence given his frail health.

The sentencing marked the latest chapter in the decline of one of the most powerful figures in Hollywood, whose reported abuse of women ignited an international movement to confront sexual harassment and assault by powerful men in the workplace.

Mr. Weinstein is one of two inmates who have tested positive for the virus at the Wende Correctional Facility, a maximum-security prison in Erie County, state officials said. They were the first among 43,000 inmates in New York prisons to be found to have contracted the disease.

Ten state corrections department staff members have tested positive, including correction officers at the Green Haven, Shawangunk, Sing Sing, Downstate and Fishkill prisons.

Before he was sent to Wende, Mr. Weinstein had been held in an infirmary unit at the Rikers Island jail complex for several days before and after his sentencing.

He left Rikers just as the coronavirus began to spread through the city jails. As of Monday, 39 inmates, 21 corrections staff and six health workers in New York City jails had tested positive.