The fire broke out in the basement of a building being used as a movie set on St. Nicholas Avenue just before 11 p.m.
While backing out of the building, the firefighter was separated from his unit and he was found unconscious
He was rushed to Harlem Hospital, where he was pronounced dead.
FDNY Commissioner Dan Nigro identified him as 37-year-old Firefighter Michael Davidson, a 15-year veteran.
Two more firefighters were seriously injured with burns, while three civilians suffered minor injuries.
Eric Phillips, Mayor Bill de Blasio's press secretary, tweeted: "This is an awful night."
The building is home to the former St. Nick's Jazz Pub, which closed in 2011.
The blaze broke out on the set of "Motherless Brooklyn," starring Norton, Bruce Willis, Willem Dafoe and Alec Baldwin.
A statement was released on behalf of the producers of "Motherless Brooklyn":
"Our deepest condolences to the family of Michael R. Davidson. A fire broke out tonight in the building where we were shooting our film. Our production was towards the end of our working day and had dozens of people working on site, when our crew noticed that smoke was coming into our set and into other parts of the building from below us. As soon as we noticed smoke coming up into our set, our crew immediately alerted the fire department and began alerting residents of the building even as we evacuated our cast and crew. To our great sorrow, we now know that a NYC firefighter lost his life battling the blaze that grew, and our hearts ache in solidarity with his family. New York City firefighters truly are the bravest in the world. We watched firsthand with astonishment as they charged into the smoke to make sure all were safely out and then fought to contain the blaze and prevent it from spreading, putting their lives on the line as they do every day. The FDNY are real life super-heroes and have our boundless admiration and gratitude."
They weren't filming when the fire broke out. The building was vacant when the fire started.
The cause of the fire is under investigation.
The Associated Press contributed to this report.