The first quake struck at 8.45am (0545 GMT) on Monday and was centred in the Aegean Sea off the coast of Izmir, the Istanbul-based Kandilli Observatory said.
It caused minor damage but no injuries.
The second quake, which struck at 12.45pm, caused further damage, smashing windows, witnesses said.
The first earthquake collapsed the walls of some houses, shattered windows in the town of Urla, just west of Izmir, and caused cracks in some buildings in the town centre.
Governor Oguz Kagan Koksal said there were no immediate reports of injuries and the authorities were evaluating the damage across the province.
In the provincial centre of Izmir, Turkey's third largest city with a population of three million people, some residents rushed into the streets in panic.
There were no immediate reports of damage in the ancient city of Ephesus, which lies just outside Selcuk, about 90km south of Izmir.
The quake also shook the Greek islands of Chios, Samos and Ikaria, but no damage or injuries were reported.
The Athens Geodynamic Institute gave a different measurement of the first earthquake's strength, saying it had a magnitude of 6.
Earthquakes are frequent in Turkey, which lies on the active North Anatolian fault.
Ruptures in the fault caused two earthquakes in August and November 1999 that killed about 18,000 people and devastated large parts of northwestern Turkey.