The shots were apparently fired from a motorcycle with two persons passing in front of the embassy, which lies on the corner of a busy highway, the police said.
Another two persons on a second motorcycle are suspected of participating in the 3:20 AM (local time) attack.
Early evidence suggests a Kalashnikov assault rifle was used, the police said.
Bullet casings collected from the scene are to be examined by Greece's anti-terrorist squad for possible matches to other attacks, the police said.
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There is strong condemnation in Greece of Israel's policies in the West Bank and Gaza, 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.
The residence of the German ambassador in Athens has been hit twice - with two assault rifles in 2013 and a rocket in 1999. Nobody inside was hurt.
In 2007, another rocket was fired at the US embassy in Athens without injuring anyone.
The group involved in the 2013 attack on the German residence, the People's Fighter Group, is still at large.