The quake struck near the Greek Dodecanese islands and the south-west Turkish coastal city of Bodrum at 1:31 am (2231 GMT), at a depth of 10 kilometres, according to the US Geological Survey.
Dozens of aftershocks were reported.
The two victims were young people who had been at a bar when the roof fell in, Giorgos Kyritsis, mayor of the town of Kos on the island of the same name, told state-run radio ERT.
The centre of Kos is home to hundreds of bars, which were packed when the earthquake struck. Three of those taken to hospital were in serious but not life-threatening condition, according to doctors cited by ERT.
A doctor at Kos' hospital said it had treated more than 100 people following the quake.
"Three people were seriously injured but are no longer in critical condition," hospital director Nektarios Georgantis told Greek television.
"Seventy-eight people have been sent home after treatment, the others have minor injuries and are being kept under observation," he said.
In Turkey, Esengul Civelek, the governor of Mugla province, where Bodrum is located, told Anadolu news agency there had been no casualties or structural damage.
Some flooding was reported in the city, however, while Turkish television showed footage of panicked people running into the streets.
Authorities had warned people to stay away from beaches, after a small tsunami was triggered.
"Don't go on beaches, don't go in damaged buildings, follow instructions by national authorities," the Paris-based European-Mediterranean Seismological Centre (EMSC) tweeted.
The harbour area in Kos was flooded, according to witnesses, damaging several boats, while social media users on the island posted pictures of badly damaged buildings and flooding.
The minarets on two old mosques and part of a church also collapsed. As day dawned, the clean-up operation began, with a plane and two helicopters arriving with rescue workers from Athens.
Kos and Bodrum are about 10 kilometres apart across the Aegean Sea.
Most European earthquakes affect Greece, the southern and western Balkans, western Turkey and Italy.
In mid-June, the Greek islands of Lesbos and Chios and western Turkey were hit by an earthquake that killed one person on Lesbos and damaged dozens of houses.
Damage caused by a quake in Kos, Greece, July 21, 2017 is seen in this still photograph uploaded on social media.
Two people were killed and scores injured early Friday on the Greek island of Kos after an earthquake of magnitude 6.7 hit the region, a local mayor said.
