Fire crews were called to the one-storey, three-flat building on Crinan Street about 1.20am.
There were multiple calls from neighbours alerting emergency services that people were in the flat or trying to go back inside it, Fire Service shift manager Brent Dunn said.
All those living in the flats are accounted for and two people were taken to hospital as a precaution for smoke inhalation.
Mr Dunn said 24 firefighters had fought the blaze which was now under control. An investigator will be at the site today.
The fire is the second in Crinan Street this month. A house was extensively damaged by a blaze on 6 December.