Greek media say around 50 bullet casings were found near Ambassador Wolfgang Dold's official residence in the Athens suburb of Chalandri in the aftermath of the attack.
Police officers guarding the residence were armed, but did not shoot back at the gunmen, reportedly for fear of hitting houses on the other side of the road during the 3.30am incident.
Four people reportedly arrived outside the house on two motorbikes and shot into the air and at the building. They appeared to deliberately avoid shooting at the security guards and no-one was injured.
Police later sealed off the area and six people have been arrested.
Afterwards Greece’s prime minister Antonis Samaras spoke with Ambassador Dold on the telephone.
The ambassador’s residence was also the target of an attack in May 1999 when a bazooka was fired at it by Marxist terrorist group 17 November.