Local authorities said the 52,400-dwt Ince Inebolu (built 2003) hit a rock at 06:44am local time on Friday and suffered minor water ingress which was under control.
No pollution has been reported and all members of the crew were uninjured.
The weather in the area was good, with the Greek coast guard already at the scene.
The Ince Denizcilik-owned vessel was en route from Yemen to Russia, without carrying any cargo.
