"I have been exposed to people in recent days who have subsequently tested positive and I had fever, chills and shortness of breath," he tweeted on Tuesday.
"I just hope I didn't give it to the kids and Cristina," he added. "That would make me feel worse than this illness!"
Mr Cuomo is quarantined at home in his basement and will anchor his CNN show from there.
"I don't care how smart, how rich, how powerful you think you are ... this virus is the great equaliser. My brother Chris is positive for coronavirus ... he's gonna be fine. He's young, in good shape, strong — not as strong as he thinks — but he's gonna be fine," the governor said.