The attack comes days before President Barack Obama is due to visit the Greek capital.
The Greek government has condemned the attack and described it as an act of terrorism.
The policeman who has been wounded was on duty outside the French Embassy when he was attacked by the unknown assailants.
No one has claimed responsibility for the attack on the building.
A police official has said: “It was probably a hand grenade.”
Government spokesman Dimitris Tzanakopoulos said: “Greek police will carry out their duty to identify the perpetrators and guarantee the protection of all citizens.
“The relations of friendship and solidarity between Greece and France can't be affected in the slightest by such terrorist acts.”
Small scale attacks on businesses, police and embassies are common in Greece with left-wing guerrilla groups often claiming responsibility.
Police shut down the area while anti-terrorism forensics searched the scene.
Authorities believe that the policeman was not badly wounded as he was inside an armoured guard post outside the embassy entrance.
A bike matching a description of the motorbike used by the attackers has been found and is being investigated by police.
Left-wing organisations have already announced that they will hold protests during Obama’s visit.
Police believe that anarchists could be behind this attack, a police source said: “Given the minor damage, it is likely a symbolic attack”.