The 65-year-old, best known for playing White House communications director Toby Ziegler in the political drama, was admitted to hospital in the US last month.
He told Good Morning Britain: “I’m an ex-smoker and I’m pre-diabetic and I’m old.
“I’m an old dude, and so I have some strikes against me, so I anticipated this was possible, but when it happened, it was really scary.”
The actor said: “I had to have the conversation with my wife, about maybe not seeing her again and because the doctor had convinced me that it was going to be touch and go.”
Schiff added: “The worst part of it is the epiphany, the realisation that you might never get to touch each other again and that for some reason struck me, struck home more than anything else.”
Schiff’s wife, Sheila Kelley, also had Covid-19.
“I have never experienced anything like this before in my life. One minute I’m feeling pretty good and the next I’m struggling to breathe,” she previously said.
The TV presenter and former X Factor judge, 68, said she was briefly in hospital with the virus.
Osbourne said she has been separated from rocker husband Ozzy Osbourne, 72, while she recovers. Ozzy has tested negative for the virus, Osbourne said.
She tweeted: “I wanted to share I’ve tested positive for Covid 19. After a brief hospitalisation, I’m now recuperating at a location away from Ozzy (who has tested negative) while The Talk is on scheduled hiatus.
“Everyone please stay safe and healthy.”
Black Sabbath rocker Ozzy has Parkinson's disease - putting him at a higher risk should he be exposed to the virus.
