Amnesty International campaigners say the decision throws the EU-Turkey migrant deal into doubt.
They say migrants in Turkey do not have basic human rights and many are at risk of being taken to Syria.
A source at the Greek migration ministry said the judges were only deciding whether the individual's case could be heard in Greece or not.
On the same day the judges' ruling emerged, Greek and EU authorities sent back 51 migrants to Turkey on boats from the islands of Lesbos and Kos
Under a deal struck between Turkey and the EU, migrants arriving in Greece are sent back to Turkey if they do not apply for asylum or if their claim is rejected.
The deal came into force in March, and more than 400 people have been sent back.
Now a Greek committee of judges has decided against sending a Syrian asylum seeker back to Turkey.
Amnesty spokesman Giorgos Kosmopoulos told the BBC that Turkey was not currently protecting migrants and refugees to the standards of the Refugee Convention. "Until it becomes a safe country nobody should be returned there," he said.
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