The fire broke out shortly before 3 a.m. on a second floor apartment in a seven-storey building on Benny Crescent.
Firefighters found the 80-year-old woman inside the apartment, unconscious, sitting in her rocking chair.
Firefighters said they believe the woman fell asleep while smoking.
She is being treated for second and third-degree burns on about per cent of her body, including her hands, arms and face.
A neighbouring building was partly evacuated.
No one else was injured.