The flames broke out on the third floor of the four-story building on Bonner Place in the Melrose section around 6:38 a.m.
The 10 victims, including a firefighter, suffered serious but non-life-threatening injuries. Some of the injured were said to be children.
There appeared to be heavy damage in the five-story building.
Some 120 fire and EMS personnel responded to the scene. The fire was brought under control in just over an hour.
A lithium-ion battery was found inside the apartment where the fire started.
No smoke detectors were present, according to the FDNY.
Fifty-six residents have been displaced.
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