A member of anarchist group Rouvikonas was arrested over the vandalism of the Parliament building earlier on Tuesday, when several hooded group members threw paint and smoke bombs on the walls.
The suspect was initially detained as he tried to flee after the attack.
The incident occurred shortly after 2 p.m. and the assailants were able to climb up the stairs beside the Tomb of the Unknown Soldier and up to the front courtyard of Parliament, which is normally out of bounds for the public.
In a post on an anarchist website, the group said the incident was a response to a decision by a judicial council not to grant furlough to Dimitris Koufodinas, the convicted November 17 assassin who went on hunger strike on May 2 in opposition to the ruling.
The head of Greece's Police (ELAS) has opened an investigation into the incident.