The fire broke out on the 3800 block of Powelton Avenue, in the city's Powelton Village section, around 11:30 on Wednesday night.
Officials say the electrical fire started on the fourth floor, knocking out elevator service.
All of the residents are sight impaired, but were able to make it out of the building.
The injured resident is being treated for a minor case of smoke inhalation.
The Salvation Army is helping the displaced residents find temporary shelter.
There's no word yet on when they will be allowed to return to their apartments.
