The van’s driver, thought to be a trafficker, fled the scene, two police officials added.
Two children were among those injured in the early morning crash on a motorway between the cities of Alexandroupoli and Komotini, the second such incident in the area this month.
The nationality of the migrants could not be immediately confirmed, but they were most likely Syrians, the officials said.
Hundreds of thousands of refugees fleeing violence in the Middle East and further afield have used Greece as a gateway to other European countries in recent years.
Thousands have arrived in recent months via the Evros river crossing in the north of the country, mostly Syrian and Iraqi families.
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