According to the statement, the blaze occurred in the Yenikale district in west Izmir in the early morning of Friday.
Turkish Health Minister Fahrettin Koca tweeted that seven people were injured in the blaze, six of whom inhaled carbon dioxide.
Kosger told a Turkish broadcaster that no one died in the incident, but the blaze completely destroyed one of the apartment blocks.
Firefighting operations were joined by 25 fire engines and helicopters from Ankara and Aydin.
The causes of the fire have yet to be determined.
Izmir Mayor Tunc Soyer tweeted that the blaze was almost extinguished, but the wooden cladding of the building was making it difficult to put out the fire.