"In these difficult times that seem to get more difficult and complicated by the day, I just found out that I am positive for coronavirus," he wrote.
He said he has experienced a fever, chills and shortness of breath, and that he fears he may have exposed his family to the virus.
Cuomo, who is the brother of New York Governor Andrew Cuomo, ended his tweet with a message of determination.
"We will all beat this by being smart and tough and united," he wrote.
Governor Cuomo spoke about the situation during his daily press conference.
"He is going to be fine. He's young, he's in good shape, he's strong, not as strong as he thinks," he said. "He'll be fine. But, there is a lesson in this. He's an essential worker, a member of the press so, he has been out there. You go out there, the chance that you get infected is very high."
Andrew Cuomo also spoke of his brother on a personal level, calling him his best friend.
"In his job, he's combative and argumentative and he's pushing people," he said. "But that's his job. He's a really sweet beautiful guy. And he's my best friend. My father was always working, so it was always just me and Chris."
He said he had fears that their mother, Matilda, may have been exposed, but that she stopped visiting before he became infected after he introduced "Matilda's Law," which requires vulnerable New Yorkers to stay home and limit home visitation to immediate family members or close friends in need of emergency assistance.
"My mother was at his house, and I said that is a mistake," Gov. Cuomo said. "Now my mother is in a different situation. She's older and she's healthy, but I said you can't have mom at the house...That's when I came up with Matilda's Law. It is clear about people who are older and what they should be exposed to. If my brother still had my mother still at his house again, out of love and comfort, and my mother wanted to be in the house anyway. She did not want to sit alone in her apartment. She would have been doing what she wanted to do. He would have wanted to do what he wanted to do, and it would have seemed great and harmless, but now we'd have a much different situation."
Watch: Governor Andrew Cuomo talks brother's diagnosis: