The fire broke out on the sixth floor of the building at 1560 Grand Concourse.
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Authorities say the three-alarm fire broke out inside apartment 603 just before 7:25 p.m. and spread to two other apartments and through the roof.
The women were pronounced dead at nearby BronxCare Health System, the former Bronx Lebanon Hospital.
All the women were older, longtime residents of the building, officials said.
A fifth woman was injured.
Fire officials have determined a space heater in apartment on the sixth floor caused the fire.
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The Red Cross is providing assistance to displaced residents.
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