In a statement, the Turkish Foreign Ministry said the attack was carried out with six molotov cocktails in the early hours of Sunday, at around 2:30 a.m local time (2330 GMT).
The statement said the attack did not cause any damage or personal injury in the consulate building.
"On the occasion of this atrocious incident, we would like to reiterate once again that we expect the Greek authorities to take necessary measures for the security of the personnel and buildings of our Missions in Greece," it added.