Gale-force winds, heavy rain and hailstorms lashed Halkidiki, near the city of Thessaloniki, late on Wednesday, officials say.
A Czech couple died when their caravan was blown away, and two Romanians and two Russians were also killed.
A state of emergency was declared and more than 100 rescue workers deployed.
Charalambos Steriadis, head of civil protection in northern Greece, described it as an "unprecedented phenomenon".
The storm followed a spell of very hot weather in Greece with temperatures soaring to 37C (98F) over the past two days.
Images and video posted on social media show trees toppled, cars overturned and buildings damaged.
"It is the first time in my 25-year career that I have lived through something like this," said Athansios Kaltsas, director of the Nea Moudania Medical Centre which treated many of the injured.
"It was so abrupt, so sudden," he said.
A witness quoted by broadcaster ERT said the freak storm had lasted only for about 20 minutes.
Severe thunderstorm in New Kallikráteia, Halkidiki, Greece last night, July 10th. Report: Forecast Weather Greece pic.twitter.com/j3TFAeEMqg
— severe-weather.EU (@severeweatherEU) July 11, 2019
A Romanian woman and her child were killed when the roof of a restaurant collapsed at Nea Plagia, officials say, while a Russian man and his son were killed by a falling tree near their hotel in the seaside resort of Potidea.
Greece's minister for citizen protection, Michalis Chryssohoidis, is due to visit the region on Thursday.
Then I noticed that the story was generated by the BBC, that just about sums it up nicely, as the BBC is part of the propaganda machine, constantly spitting out phrases like "global warming " and "Climate change ".
Seems strange the amount of investment these organisations have yet continue to be unable to predict the weather with any consistency, or accuracy.
This event didn't just happen, converging air masses don't sneak up on each other, satellite images would have clearly illustrated them and given the disposable energy in Earth's atmosphere, powerful storms result.