As he delivered the news, his younger brother, Chris Cuomo, 49, a CNN anchor, announced that he had tested positive for the virus. The governor later said his brother had a fever, shortness of breath and chills.

The governor has appeared on his brother’s show regularly since the outbreak began, offering their sibling rivalry to viewers as a humorous diversion from the drumbeat of grim news.On Sunday night, the governor even teased his brother for broadcasting from his basement, where, it turns out, the younger Mr. Cuomo was quarantined as of Tuesday.

“Everyone is subject to this virus,” the governor said on Monday. He added that his brother, whom he called his best friend, was strong — “not as strong as he thinks” — and that he would be fine.

Mr. Cuomo has invoked his family throughout the crisis as a reference point for others about how the disease was affecting their loved ones. But Tuesday was the first time the governor spoke about the disease striking his own family.

He used his brother’s illness to demonstrate the importance of social distancing, even from family members, saying that two weeks ago he had talked his brother out of letting their mother, who lives alone, stay at his house.

“If my brother still had my mother at his house,” he said, “chances are she may very well have been exposed, and then we would be looking at a different situation than just my brother sitting in his basement for two weeks.”

More updates from Tuesday:

The daily number of new deaths in New York State has increased 31 percent a day on average for the past week, and the death toll has tripled in four days.

The statewide number of confirmed cases increased by 9,298, to 75,795.

The number of patients hospitalized passed 10,900, up 15 percent from Monday. Of those, 2,710 were in intensive care rooms with ventilators.

Gov. Philip D. Murphy of New Jersey announced 2,196 new virus cases, bringing the state’s total to 18, 696. There were 69 new fatalities, including two men in their 30s, bringing the total to 267.

Gov. Ned Lamont of Connecticut announced 557 new virus cases, bringing the state’s total to 3,128. Thirty-three more people had died of the virus, bringing the number of fatalities to 69, state health officials said.

The Elmhurst doctor featured in a video report has tested positive.

Last week, with Elmhurst Hospital overwhelmed by the coronavirus crisis, Dr. Colleen Smith took The New York Times inside the emergency room, filming the struggle that she and her colleagues faced trying to treat the surge in patients.