The vast majority of the people under monitoring are under voluntary home isolation.
The Department of Health is also asking any New Yorkers who return from China, Iran, Italy, South Korea or Japan to self-isolate for 14 days as a precaution.
"As New York City continues to see more cases, I am reminding New Yorkers to remain vigilant, but not alarmed," said Mayor Bill de Blasio. "We are continuing to do everything in our power to keep New Yorkers safe and healthy, and are asking our federal partners to help us increase testing capacity so we can get the job done faster."
In addition, Health Commissioner Oxiris Barbot is ordering any educator, healthcare worker or first responder employed by the city, the Department of Education and the New York City Health + Hospitals Corporation who the Department determines presents a danger of infection to others to submit to testing for COVID-19.