It happened in the Greenpoint section just before 4:30 a.m. Tuesday.
Fire officials say the blaze started in a location on the second floor of the building.
One building resident suffered serious injuries and was taken to an area hospital.
The cause of the fire is under investigation.
The blaze comes about an hour after crews battled another fire in the Bay Ridge section.
An unoccupied home on Shore Road Lane, which appeared to be under renovation, caught fire around 3:15 a.m.
No injuries were reported and crews were able to douse and put out the flames about an hour later.
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