One of the men, from the flat where the fire broke out, suffered burns while the others suffered smoke inhalation. Both men and one of the women were taken to the Southern General Hospital for further treatment.
A fire service spokesman said: "This incident shows fire can strike anywhere at any time. Thankfully we are not talking about a tragedy but the injuries, memories and damage to property can be extremely traumatic for the people involved.
"Although the fire was confined to the first-floor property, this incident resulted in significant smoke damage to flats throughout the building. That is a stark reminder of the danger smoke presents and the vital need for every household to have at least one working smoke alarm, which will give families the time they need to get to safety."
The spokesman said the cause of the fire is not thought to be suspicious.