Two Kalashnikov assault rifles used in the attack had been used in a similar attack on the residence of the German ambassador last December by the People's Fighter Group, a police source said.
The Israeli government blamed the attack on a "hate campaign" by Palestinian authorities over the death of a Palestinian official in a confrontation with Israeli soldiers in the West Bank on Wednesday.
"The international community should condemn this campaign and its consequences," the Israeli foreign minister said in a statement.
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 neighbouring petrol station told reporters.
Another two people on a second motorcycle were suspected of also taking part in the attack.
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."
"Every terrorist attack is an assault on democracy and the country," said government spokeswoman Sophia Voultepsi, who added the Athens was taking "determined steps" against terror groups.
The People's Fighter Group had also fired on the offices of the ruling conservative New Democracy party in January 2013.
Israel's policies in the West Bank and Gaza have been widely condemned in Greece, with many protests held in support of the Palestinians.
Embassies and diplomatic vehicles in Greece have been targeted in attacks by far-left groups in recent years.
In 2007, another rocket was fired at the US embassy in Athens without injuring anyone.
All three attacks were claimed by far-left groups, two of which have since been dismantled by the police.
