Crews responded to the 200 block of North 57th Street shortly after 1:00 p.m.
The building was evacuated and residents were taken to a nearby church.
The fire was brought under control within 30 minutes.
So far, there is no report on injuries.
The Red Cross is assisting 37 displaced residents. Officials say most of them will be able to return to their apartments.
The cause of the fire remains under investigation.