The police said the envelope from Italy contained a makeshift explosive device and was addressed to a senior Greek police officer.
The bomb apparently went off by accident after the envelope was dropped by staff at a post sorting centre north of Athens, the police said.
Similar devices had been sent by the Italian Informal Anarchist Federation (FAI) to the then justice minister and the warden of Greece's top security prison in 2011.
FAI has expressed solidarity to jailed members of Greek militant outfit Conspiracy of Fire Nuclei, which had sent parcel bombs to European leaders and embassies and carried out arson and bomb attacks some three years ago.