Ankara had previously said it would conduct a "seismic survey" (deep sea research technique) in the south and east of Kastelorizo island, off the coast of Turkey, in the eastern Mediterranean.
The Greek newspaper, "ekathimerini", which reported the army's alert, said it was noticed that the activity had increased in the nearby Turkish "Aksaz" naval base.
She noted that 15 naval groups left the military base, which raised suspicions with the authorities in Athens and the Greek navy.
The Greek army chief shortened his trip to Cyprus because of this development.
Berlin had earlier called on Ankara to stop drilling for natural resources in the water in the eastern Mediterranean.
German Foreign Minister Heiko Maas said that if Turkey wanted to make progress in its relations with the European Union, it should stop these activities.
