The blast in Kusadasi, 72km southeast of the port city of Izmir, tore off the roof and sides of the bus.
Thirteen people, including six Britons, were wounded.
There were no immediate claims of responsibility for the blast.
A police official in Kusadasi said evidence suggested that the bomb went off where a female passenger was seated, which has led to speculation that it could have been the work of a female bomber.
The official, who spoke on condition of anonymity, said the woman was a Turkish citizen.
Another police official said the bomb could have been placed under the woman's seat.
Ali Baris, the governor of Kusadasi, said the blast occurred as the minibus travelled through the town square but could not confirm the cause.
Irish fatality confirmed
Baris said the explosion left several of the wounded in critical condition.
A spokesman for Ireland's Department for Foreign Affairs said: "We are confirming that there is one Irish fatality - a young woman student was caught up in the blast."
Thirteen people were wounded in
the blast, mostly Turkish citizens
The United Kingdom's Foreign Office has also confirmed that one of its citizens had died.
The other victims were identified as Turkish citizens.
A doctor at Kusadasi State Hospital said five wounded tourists were transferred to Izmir for treatment.
The doctor and the police officials spoke on condition of anonymity because Turkish civil servants are not permitted to speak to the media without prior authorization.
British tourists injured
The British Foreign Office in London said five Britons were seriously injured and one suffered minor injuries in the blast. No details of the injuries were given.
Police Chief Yilmaz Orhan of Aydin province, which includes Kusadasi, said the British tourists were the only foreigners injured in the blast.
Police say the explosives could
have been placed under a seat
Speaking shortly after the explosion, Prime Minister Recep Tayyip Erdogan said Turkey was taking anti-terror measures but added that "it is not possible to stop it 100%, no matter how strict security measures you take".
Civilians ran to the bus after the blast and carried the injured away from the burning wreckage.
According to private NTV television, police suspect that C-4 plastic explosives were used in the blast.