The fire tore through the second floor of the Ludlow Street building just before 11:30 a.m.
Officials said the woman, Claudete Rivera, was pronounced dead at the scene.
Investigators said Rivera was using the burners on stove to stay warm. Her clothes caught fire, officials said.
Investigators say a neighbor who rushed into the apartment to try to help suffered minor burns and smoke inhalation.
No one else was injured.
Firefighters got the flames out in minutes, but too late to save Rivera.