Kos Mayor Giorgos Kyritsis told state-run Greek media that buildings on the island sustained structural damage. He didn't give further details on the deaths and injuries.
The coast guard also announced the island's port was damaged in the quake and that a ferry en route there was not docking.
The fire department separately said three injured people had been rescued from rubble on Kos.
Eyewitnesses said there were several aftershocks up to a magnitude of 5.8, while social media users posted videos of locals cowering for cover.
According to Turkey's disaster and emergency management service, an earthquake of magnitude 6.3 occurred and was felt in Mugla and its surrounding areas.
Others told how sea levels dipped by about a foot before the tsunami struck, followed by mass floods shortly after.
The tremblor, initially reported as a magnitude 6.9, was very shallow, only 10km below the seabed.
A magnitude 6.7 quake is considered strong and is capable of causing considerable damage, but today's tsunami would have been dampened by seas.
Turkey is prone to earthquakes because it is located between the Arabian plate and Eurasian plate.
- additional reporting by AP
