The fire broke out on the first floor of the Nostrand Avenue building in Flatbush just after 4 a.m. on Monday.
One person died at King County Hospital. The victim may have jumped out of a window in an effort to escape the flames.
"I did see someone jump out from the building, they jumped from the third floor. He jumped onto the landing right there and onto the floor," the witness said.
Three others are in serious condition. Four people suffered minor injuries, including a police officer.
The injured are being treated at SUNY Downstate Hospital and Brookdale University Hospital.
The cause of the fire is under investigation.