Four of the victims are a family of tourists from the United States, and the other two are an elderly couple who lived in the building.
The explosion, which occurred on Friday morning in a two-story building in the tourist-heavy Plaka area at the foot of the Acropolis, was likely caused by a gas leak, said the Greek capital's mayor, Haris Doukas.
The American family had rented the apartment and had planned to travel home to the United States later on Friday, local media report.
Several buildings and cars around the building were damaged when the house collapsed in the explosion. Two women in an adjacent building were taken to hospital and another person was slightly injured by debris.
