The Athens Geodynamic Institute says the quake with a preliminary magnitude of 5.8 struck at a depth of 37 kilometers (23 miles) in the Aegean Sea at 3:44 p.m. (1244 GMT) on Sunday. That is between the Greek island of Rhodes and western Turkey.
Turkey's Kandilli Observatory gave a stronger preliminary magnitude of 6.0, with aftershocks of 4.9 and 4.7. areas of Turkey shaken by the quake included the popular Aegean resort town of Oludeniz, the Aegean port of Izmir, and the Mediterranean city of Antalya.
Police in Rhodes said there are no reports of injuries or damage.
No serious casualties were reported in Turkey either, but officials said half a dozen people who jumped out of windows in panic over the temblor were injured.
These regions of Greece and Turkey are in seismically active areas and suffer frequent earthquakes.