Two petrol bombs have been thrown at a culture ministry building in central Athens, say police.
Security is tight in Athens ahead of the Olympic Games
No one was injured in the attack on the building which has featured a four-year Olympic exhibition running up to the Games in August.
There was no claim of responsibility or motive, but anarchists, who have carried out hundreds of similar attacks, are thought to be to blame.
Previous targets have been businesses, banks and diplomatic vehicles.
There have been a number of attacks linked to the Olympic Games in recent months.
A small bomb was found at a car dealership in a southern suburb of Athens in June and three bombs exploded outside a police station in the city on 5 May.
A Greek extremist group said it had carried out those attacks, criticising security for the Games, which start on 13 August.
Greece has prepared the largest ever Olympic security operation in the history of the Games, spending up to one billion euros ($1.3bn, £600m) on 40,000 policemen, guards and troops.