A search and rescue operation involving patrol boats, a helicopter and divers was underway for potentially missing people, the coast guard said late on Tuesday.
Another 24 migrants were rescued and transported to a hospital on Chios, as were two coast guard officers who were injured in the incident. It was unclear how many of the survivors transported to the hospital had been injured.
The coast guard said it was not immediately clear how many people had been on the speedboat, and a search and rescue operation involving four patrol vessels, an air force helicopter and a private boat carrying divers was underway for potentially missing passengers.
Video footage by a local news site showed at least one person being carried in a blanket from a coast guard boat moored on the side of a jetty into a waiting coast guard vehicle with blue flashing lights, as others appear to lead two children toward the car.
The coast guard did not immediately have further information on exactly how the collision occurred, or on the identities of the casualties or the other passengers on the speedboat.
Greece is a major entry point into the European Union for people fleeing conflict and poverty in the Middle East, Africa and Asia.
Fatal accidents are a common occurrence.
Many undertake the short but often perilous crossing from the Turkish coast to nearby Greek islands in the eastern Aegean.
But increased patrols and allegations of pushbacks - summary deportations without allowing for asylum applications - by Greek authorities have reduced crossing attempts.
Greece, along with several other European Union countries, has been tightening its regulations on migration.
In December, the European Union was overhauling its migration system, including streamlining deportations and increasing detentions.
There has long been a fierce debate among EU members about migration.
Since a surge in asylum-seekers and other migrants to Europe a decade ago, public debate on the issue has shifted and far-right parties have gained political power.
EU migration policies have hardened, and the number of asylum-seekers is down from record levels.
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