A bomb has wrecked several parked cars near the Athens home of Greek Culture Minister Giorgos Voulgarakis.
Police said 2-3kg of dynamite was used in the attack
The blast happened at the time when Mr Voulgarakis would normally have been passing by on his way to work. Nobody was hurt by the explosion.
Mr Voulgarakis headed the law and order ministry before moving to culture this year. The move was seen as a demotion following a phone-tapping scandal.
So far no-one has said they carried out the attack.
A police official told the BBC the minister was clearly the target.
Mr Voulgarakis said this was an "attack against democracy"
Mr Voulgarakis was unscathed on Tuesday morning because he had been delayed by a few minutes.
At least five cars were damaged in the explosion.
Police told Reuters news agency the device contained 2-3kg (4-7lb) of dynamite and was strapped to a bicycle seat near a car. Other reports said the device was under the car.
Mr Voulgarakis said: "It was an attack against democracy. I have complete confidence that the Greek police will do their job."
Mr Voulgarakis, 46, was moved to the culture ministry in a cabinet reshuffle this year after a controversial period as minister of public order.
In February he and other key ministers were forced to admit that the mobile phones of most of the cabinet and top security officials had been tapped in 2004 - the year of the Athens Olympics.
The BBC's Richard Galpin in Athens says it is widely believed American intelligence agents were responsible.
Mr Voulgarakis had also been criticised for categorically denying allegations last year that a group of Pakistani men in Athens had been abducted and interrogated by Greek and foreign intelligence agents over possible links to terrorist groups.
A prosecutor has since upheld the allegations.
Although no-one has yet claimed responsibility for Tuesday's bomb attack, left-wing extremists are likely to come under suspicion, our correspondent says.
Bomb attacks have become rarer since the conviction of the leaders of the November 17 guerrilla group prior to the Athens Olympics.