Ten of those 11 cases stem from the same attorney from Westchester who tested positive for the novel coronavirus.
Cuomo said someone who came into contact with the Westchester man has tested positive, as well as that man's wife and their three children. One other daughter in the family tested negative.
"The not-so-good news is that there was another person being tested who came in contact with the lawyer, a friend of the lawyer who spent time with and in close proximity in close situations," Cuomo said.
The new family is associated with the Westchester Torah Academy in White Plains, which is closed through at least Friday.
WATCH: Gov. Cuomo gives coronavirus update in Westchester
The governor announced earlier Wednesday that the wife, 20-year-old son, 14-year-old daughter and neighbor of the Westchester man who initially tested positive have also all tested positive.
Cuomo said the neighbor is the person who drove the infected man to the hospital, therefore he was in an enclosed space with the man.
"There are going to be hundreds in Westchester," Cuomo said of his expectation going forward. "The number of people who will be infected will continue to increase. It is going to be dozens and dozens and dozens."
The Westchester County cases are suspected to be from "community spread."
The New Rochelle man in his 50s with an underlying respiratory illness is hospitalized in critical but stable condition at New York-Presbyterian/Columbia University Medical Center in Washington Heights, the New York City Health Department said.
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Initial review of his travel does not suggest any direct connection to China or any country on the watch list. He did travel to Miami and Israel during the past few months, but not during the two week incubation period.
He returned to Westchester some time ago and started showing serious symptoms last week. Officials say he had respiratory issues for the last month, became they more pronounced in the last couple of days.
The wife, children, and neighbor are all isolated in their homes. The 14-year-old girl is a student at SAR Academy in Riverdale.
Mayor Bill de Blasio said the wife and daughter are asymptomatic.
The son did show symptoms but is getting better. A close friend and roommate of his have been tested out of precaution. Those results are pending.
Seven employees and one intern at the law firm where the man and his wife work are also being tested.
Yeshiva University announced the son tested positive on Wednesday.
Westchester Day School in Mamaroneck, Westchester Torah Academy in White Plains, and alanter Akiba Riverdale (SAR) Academy and SAR High School in Riverdale, Bronx are all closed. The schools are associated with the Westchester County cases.
Temple Young Israel in New Rochelle, where the patients are congregants, has been ordered to suspend services for the foreseeable future. Some congregants have been ordered to self-quarantine due to possible exposure.
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The first positive case in the state was confirmed last Sunday. The 39-year-old health care worker from Iran was said to being doing better and was believed to be quarantined in her Manhattan apartment. Her husband had been tested for coronavirus, but that test has since come back negative.
De Blasio said they will, however, treat the case as if he tested positive and he will remain in quarantine.
The governor said two families in Buffalo who recently returned from Italy tested negative for the virus.
The governor estimated about 1,000 people are self-quarantining across the state in response to coronavirus.
Cuomo signed a bill Monday to direct $40 million to help the state hire more staffers and buy equipment to help respond to coronavirus. The legislation also gives the governor the authority to declare a statewide disaster emergency for an urgent disease outbreak and temporarily suspend state and local laws and regulations to cope with it.
Cuomo said there are 300 CUNY and SUNY students plus faculty who will return from study abroad programs in five countries -- China, Italy, Japan, Iran, South Korea. They will be flown into Stewart Air Force base and quarantined in their dormitories for 14 days when they return.
The city's Department of Education is canceling overseas trips to afflicted countries.
All 1,800 public schools will require "deep cleaning" twice a week. Students with symptoms will immediately be isolated, given a mask and "taken to a doctor right away." School attendance "has not moved one iota" since coronavirus came to public attention, the mayor said.
Cuomo said the state public health laboratory is teaming up with hospitals with a goal of ensuring the state can handle up to 1,000 coronavirus tests per day.
He also said New York will institute a new cleaning protocol at schools and in the public transportation system.
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