The blast occurred at a café in the affluent Alsancak area of the Aegean port city.
“Two grenades were thrown into the cafe and exploded, but the attack has no political links,” Izmir police chief Huseyin Capkin told reporters. He did not give details.
The explosion comes as General Yasar Buyukanit, the Turkish army’s chief of staff, rejected the unilateral ceasefire offer made by the separatist Kurdistan Workers party (PKK).
Far-left and Islamist groups have also carried out bomb attacks in Turkey in the past.
Ankara blames the PKK for the deaths of more than 30,000 people since the group launched its armed struggle for an independent Kurdish homeland in southeast Turkey.