Twenty-one people were taken to hospital with suspected smoke poisoning, but no one was seriously injured, said the emergency services. Three people received in-patient treatment.
More than 200 firefighters tackled the blaze. Several troops of firemen with breathing apparatus went in to rescue the inhabitants of the flats.
About 20 people had to spend the night in a nearby school, the others stayed with relatives or friends.
After the blaze was put out at about 3:00 am, firefighters remained to ensure that the fire was completely extinguished.
The roof of the 11 floor building in the Olympic Village district was badly damaged.
It was not yet clear what caused the blaze, but it is suspected that some gas cylinders which were stored on the roof may be to blame.