It happened around 8:00 p.m. Sunday at the University Square Complex located at 40th and Market streets.
The fire was first reported from the 7th floor of the building.
A 98-year-old woman suffered smoke inhalation. She was taken to the Hospital of the University of Pennsylvania in stable condition.
Fire crews quickly brought the blaze under control. No one else was injured.
The cause of the fire remains under investigation.