Cuomo said the state health department would soon issue regulations requiring colleges to notify health officials when they have 100 confirmed cases, which could prompt a switch to remote learning for at least two weeks.
SUNY Oneonta announced last week that it was moving all students to remote learning off-campus for the fall semester due to an outbreak. The college had 651 confirmed cases by Monday.
The governor said at a briefing that six other colleges in New York had seen outbreaks: Cornell University, University at Buffalo, Hofstra University, SUNY Oswego, Colgate University and SUNY Fredonia.
Each of those schools was reporting fewer than 100 cases Tuesday.
"In New York, we have a problem," Cuomo said.
The governor said the virus is being spread at parties, some attended by students from states on New York's quarantine list.
He was especially critical of authorities allowing New York University students, many without masks, to socialize in Manhattan's Washington Square Park this past weekend.