People poured onto the streets in panic in Izmir city, witnesses said, after the quake struck with a magnitude of up to 7.0.
Izmir mayor Tunc Soyer said around 20 buildings had collapsed in the province. Izmir's governor said 70 people had been rescued from under the rubble.
Crisscrossed by major fault lines, Turkey is among the most earthquake-prone countries in the world. More than 17,000 people were killed in August 1999 when a 7.6 magnitude quake struck Izmit, a city southeast of Istanbul. In 2011, a quake in the eastern city of Van killed more than 500.
Footage on social media showed debris including refrigerators, chairs and tables floating through streets on the deluge. TRT Haber showed cars in Izmir's Seferihisar district had been dragged by the water and piled on top of each other.
"We have never experienced anything like it," said George Dionysiou, the local vice-mayor. "People are panicking." A Greek police spokesman said there was damage to some old buildings on the island, with no immediate reports of injuries.