Authorities were investigating the incident which took place around 3:30 am.
"There was extended damage," said the official who declined to be named. There were no injuries.
Arson attacks are not uncommon in the country which has a history of political violence.
Athens and Ankara, NATO allies, are at odds over various decades-old issues ranging from mineral rights in the Aegean Sea to ethnically split Cyprus.
A recent deal between Turkey and Libya over maritime boundaries has angered Greece, which sees the move as infringing its own sovereign rights.