The Greek navy said the Turkish merchantman ship had "approached and touched" one of its gunboats, which was taking part in a NATO exercise.
After the collision the merchantman fled back towards Turkish waters, the navy said.
"Nobody was hurt and no serious damage was caused," it added.
Turkey has for decades disputed Greek sovereignty over Aegean waters and airspace close to Turkish shores, which Athens says is based on postwar treaties.
The two countries nearly went to war over a cluster of uninhabited islets in 1996, and mock dogfights between the two airforces are common.
Last month, a Greek fighter pilot died when his plane crashed in the Aegean while returning from a mission to intercept Turkish jets.
A few days earlier, Greek soldiers had fired warning shots at a Turkish helicopter after it approached the small island of Ro, which is on Greece's border in the Aegean's southeast.
There is also tension over Greece's refusal to extradite eight Turkish soldiers who sought refuge in the country after the failed 2016 army coup against Turkish President Recep Tayyip Erdogan.
The Greek Supreme Court has ruled against extradition, arguing that they would not receive a fair trial in Turkey.
In turn, Turkey has refused to release two Greek soldiers who were caught in March after crossing the border, claiming to have lost their way in the fog.
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