More than 30,000 people join rally against austerity plans as services grind to a halt.
Police said it was not immediately clear what the target was but anti-terrorism police were investigating the scene.
The blast also damaged nearby cars and adjacent buildings.
Radical left-wing and anarchist groups often carry out bombings in Athens, but most are small and cause no injuries.
Sunday’s explosion was the first in years to kill someone.
However, some groups have been escalating attacks recently.
Self-proclaimed guerrilla group Fire Conspiracy Cells claimed responsibility just last week for three small-scale bomb attacks against a police detention centre, a far-right nationalist group called Golden Dawn, and the home of a leading member of the Pakistani community, all within a space of 30 hours.
On January 10, a small explosive device went off outside the Greek parliament in Athens, prompting George Papandreou, the prime minister, to condemn the attack and vow that “democracy will not be terrorised”.
Fire Conspiracy Cells also claimed responsibility for that blast, which did not cause any injures.