City officials say the cases, occurring in the past two months, are the first such concentrated cluster.
Leptospirosis is a bacterial infection that is most commonly spread by contact with rat urine and is very rarely spread from person to person.
The illness is serious but it can be treated with common antibiotics.
A disease spread by rats has been blamed for killing one person and sickening at least two others in a building in the New York City borough of the Bronx, reports CBS New York.
There are typically one to three cases of leptospirosis every year in New York City.
Two of the cases of Leptospirosis were identified in December, with a third case reported in February.
Leptospirosis is caused by a spiral-shaped bacterium known as Leptospira, which can infect animals and people.
All three victims had severe illness and were hospitalized with acute kidney and liver failure, the alert says, while one person who developed a pulmonary hemorrhage died as a result of an infection it caused.
Between 2006 and 2016, there were only 26 cases of leptospirosis reported among New York City residents.
The bacteria enters the body through open cuts and wounds, or through the nose, eyes or mouth. Some people who are infected may have no symptoms, while others may have a mild illness with fever, headache, chills, muscle aches, vomiting or diarrhea. As such, city agencies have taken "immediate measures" to reduce the rat population in the area and are spreading the word about symptoms and treatments to tenants. Additionally, washing hands thoroughly after any contact with areas where rats may have urinated is recommended.