The early morning attack was similar to the shooting of a policeman in January, claimed by the People's Revolutionary Struggle (ELA). That officer survived.
In Wednesday's shooting, the victim was part of a police protection unit guarding the home of Sofia Kyriakidou, who testified in a trial against her ex-husband, Angeletos Kanas, a member of the ELA group.
Four members of the group were sentenced in October 2004 to 25 years in jail but later released, mostly on health grounds.
A police official who requested anonymity said: "He was sitting in his car, on duty guarding a witness when he was attacked."
The unidentified attackers disappeared on the streets of Patissia and a hunt is under way to find them.
Left-wing and anarchist guerrilla groups have launched a number of attacks against the police and business targets since an officer shot dead a teenager in Athens in December, prompting the worst riots in decades.
"We are investigating whether one of these groups was behind the shooting," the police official said.
There was no immediate reaction from the government.
The ELA formed in 1974 and specialised in striking police, banks, government offices and US interests. It ceased its activities in 1995 after about 250 attacks.