School officials say they all live in the freshman dorm, Rubin Hall, in Greenwich Village.
All 400 residents in the building have been asked to quarantine until at least the end of Tuesday.
This comes about one week after a large crowd gathered in nearby Washington Square Park, with some not wearing masks.
The university says that since August 1, NYU has conducted nearly 26,000 tests, with a positive rate of 0.12%.
In a statement, the school said, "We are arranging for meals and other supports for the quarantining students. All of NYU's courses this fall 2020, regardless of whether they meet in person, are structured to have the capacity for students to attend remotely, so students will be able to keep up with their studies.
"The University is committed to the health and safety of its students, and has and will continue to communicate regularly with the students and with their families."
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