It started just before 9 p.m. at a building on Mulberry Street in Chinatown.
The FDNY said that one person was seriously injured.
Officials say the blaze broke out on the fourth floor and flames spread to the fifth floor.
The building is home to a senior center, a dance center and an immigrant services organization.
Mayor Bill de Blasio responded to the fire on Twitter, saying, “I know the neighborhood is in shock tonight. We’re going to help the community get through this.”
It’s not clear whether anyone was inside when the fire broke out, but a witness told CBS2’s Lisa Rozner it sounded like an explosion at first.
The cause of the fire has not yet been determined.