Two Kalashnikov assault rifles used in the attack had been previously used in a similar attack on the residence of the German ambassador last December by the People's Fighter Group, a police source said.
A gunman riding on the back of motorcycle fired at least 54 rounds from a Kalashnikov rifle, police said, as it passed the embassy, which sits on the corner of a busy road in the affluent northern suburbs of the Greek capital.
Television footage showed bullet holes on the side of the embassy building. "There were two bursts of gunfire... they must have emptied an entire clip," the attendant of a neighboring gas station told reporters.
Another two people on a second motorcycle were suspected of also taking part in the attack, which happened at 3:20 am.
Public Order Minister Vassilis Kikilias, who visited the scene, told the Ana news agency, "No one is going to affect the relations between Greece and Israel."
Relations between the two have warmed considerably recently as tensions have risen between Israel and Turkey, once a close ally of the Jewish state.
"Every terrorist attack is an assault on democracy and the country," said government spokeswoman Sophia Voultepsi, who added that Athens was taking "determined steps" against armed terror groups.
Embassies and diplomatic vehicles in Greece have been targeted in attacks by far-left groups in recent years. The People's Fighter Group had also fired on the offices of the ruling conservative New Democracy party in January 2013.
In 2007, another rocket was fired at the US embassy in Athens; no one was injured.
All three attacks were claimed by far-left groups, two of which have since been dismantled by the police. But the People's Fighter Group remains active and its members at large.