The fire started in the building on the corner of Commonwealth and Bronx River avenues in Van Nest at about 5:30am and spread to multiple floors.
At least 12 people have been injured and while none of the casualties are thought to be in a life-threatening condition, further details of the injuries are not known.
According to local reports, the fire started in a furniture store on the ground floor before quickly spreading throughout the four-storey building.
Images from the scene show smoke billowing out of the apartment block and the New York Fire Department (FDNY) has urged those living nearby to avoid the smoke.
More than 20 fire appliances are on the scene and more than 100 firefighters are desperately trying to extinguish the blaze.
The blaze comes several days after another fire in the borough, started by a 3-year-old playing with a stove, claimed the lives of 12 people, including four children.
The boy’s mother quickly rushed the family out of the building when the fire took hold, but did not close the door to her apartment which allowed the blaze to spread rapidly.
In a press conference on Friday, FDNY Commissioner Daniel Nigro told reporters the stairway “acted like a chimney”.
He added: “It took the fire so quickly upstairs that people had very little time to react.”
New York Mayor Bill de Blasio mourned the “horrible, tragic accident”, which has become the deadliest blaze the city has seen for decades.