Harvey Weinstein, the disgraced film producer who was convicted of two felony sex crimes in a case that helped start the #MeToo movement, has contracted the coronavirus, according to two people with knowledge of the matter.

Mr. Weinstein tested positive for the virus and was being held in isolation Monday at the Wende Correction Facility, east of Buffalo, according to the two people, who spoke anonymously because they were not authorized to talk to reporters.

One of the people said the producer did not have symptoms and was under close observation. It was not clear why he had been tested.

Mr. Weinstein falls squarely within the category of infected people for whom experts say the disease could be dangerous. He is 68 and has had a series of health problems in recent months.

He was hospitalized twice in the jail ward at Bellevue Hospital Center for high blood pressure, heart palpitations and chest pain — once after his conviction and once after his sentencing. During his first stay there, he had a procedure there to alleviate a blockage near his heart.

Late on Sunday, Michael Powers, president of the New York State Correctional Officers and Police Benevolent Association, told Reuters that he learned the formerly powerful producer had tested positive for the virus. Mr. Powers did not respond to requests for comment on Monday.

Mr. Weinstein’s positive test was first reported by The Niagara Gazette, a newspaper in Niagara Falls, N.Y.

Mr. Weinstein’s lead counsel, Donna Rotunno, declined to say on Monday whether Mr. Weinstein had tested positive. “We are going to protect Mr. Weinstein’s privacy,” she said in a statement.

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.

Several inmates in the Rikers facility where Mr. Weinstein was housed last week have tested positive for the disease, according to a third person with knowledge of the city jails, who spoke anonymously for fear of retributions at work.

It remained unclear if Mr. Weinstein’s illness would delay efforts by prosecutors in Los Angeles to extradite him to stand trial there on charges that he raped one woman and sexually assaulted another in February 2013.

On Monday, even as reports about Mr. Weinstein contracting the virus were published, the Los Angeles district attorney’s office made a official request to New York State for temporary custody of Mr. Weinstein to bring him to Los Angeles, a spokesman for the office, Greg Risling, said.

“As for any concerns given the coronavirus pandemic, our office expects that each agency responsible for processing, transporting and housing defendant Weinstein will follow its protocols and public health guidelines,” Mr. Risling said.

On Feb. 25, Mr. Weinstein was found guilty of raping Jessica Mann, an aspiring actress, in a Midtown Manhattan hotel in 2013, and of forcibly performing oral sex on Miriam Haley, a production assistant, in his apartment in 2006.

The jury acquitted Mr. Weinstein on the most serious charges against him: one count of first-degree rape and two counts of predatory sexual assault.