The 1,600-dwt Kerem S (built 1984) got stuck on 20 February off Patmos after engine failure.
Its crew of six were rescued by a coast guard helicopter.
But the vessel was blown off the rocks in bad weather on Thursday, local reports said.
No pollution has so far been reported.
The vessel was managed by Efe Gemi Isletmeciligi Sanaya of Istanbul.
