The fire started in the kitchen of the home on Findlay Avenue just before 9 p.m.
Video from Citizen App showed flames shooting from the apartment building.
The boy suffered severe burns and smoke inhalation and was rushed to Bronx Lebanon Hospital in critical condition.
Eight children and an adult were in the apartment at the time of the fire. None of the others was hurt.
A firefighter was treated at the scene.
FDNY Fire Marshals deemed the fire accidental, caused by an electrical issue with the refrigerator.
They said a smoke alarm was present and activated.
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