The 68-year-old convicted rapist - who was sentenced to 23 years in prison after he was found guilty of third-degree rape and a first-degree criminal sexual act earlier this month - is said to still be in medical isolation in prison and is now "mending".
A source told Deadline: "He is fine.
"He is over the hump and just mending."
Earlier this week, Weinstein was reported to have been one of two people to test positive for the virus in New York's Wende Correctional Facility, just days into his 23-year sentence.
A source said at the time: "He tested positive and is quarantined."
Weinstein is said to have been isolated at the prison, while a representative for the movie mogul said they were not aware of the diagnosis.
The Department of Corrections and Community Supervision were not able to say who had tested positive because of federal health-care privacy law, but they did confirm that two had tested positive for the coronavirus.
What's more, it has been claimed the disgraced movie mogul wants to postpone his civil case by two months.
He is being sued by actress Wedil David, who accused him of sexually assaulting her in 2016, but his legal team have asked the judge for an eight-week extension "due to the current coronavirus crisis" that is sweeping across the globe.
According to the court documents, his lawyer has claimed there are several reasons why the former movie producer can't meet the deadline; including his recent conviction in his New York rape case, his forthcoming criminal case in Los Angeles, and his declining health and on-going medical problems.
After Weinstein was sentenced, he was rushed to hospital after suffering a "dangerous" rise in blood pressure following his sentencing hearing.