Police said that the teenager and her mother and sister were probably walking past the building when the bomb placed in a bag went off in the city's busy Patissia district at 10:50 pm (local time).
While boy died on the spot and his sister was critically wounded, his mother is said to have escaped with minor injuries.
The victim's sister has been rushed to a nearby hospital for treatment.
The area have been cordoned off by the Greek anti-terrorism police.
The explosion is one of the rare incidents when the blast took place without any warning calls for police to clear the area.
Bomb attacks on public buildings and business, which is frequent in Athens and the northern city of Salonikain usually carry warnings before the explosions take place.
On Oct 2009, six policemen were killed in a machine gun attack on a police station.
Ever since a youth was killed in Dec 2008, Greek has faced a series of attacks targetted against places economic interests and offices of politicians.