Firefighters rushed to Norway Gardens, in Dunfermline, at around 12.35am after a blaze broke out in its stairwell.
Among the six people rescued were two girls, aged nine and 13, who were given oxygen as they were suffering from the effects of smoke inhalation.
An elderly woman, who was also suffering from smoke inhalation, was passed to the care of ambulance crews.
Firefighters had the blaze under control by 2.43am.
The Scottish Fire and Rescue Service said an investigation would be carried out later today.