The blast, which police believe was carried out by domestic guerrilla groups, is the first such incident since leftist Prime Minister Alexis Tsipras came to power in January. There was no immediate claim of responsibility.
Attacks against banks, politicians and business people are not uncommon in Greece, which has a long history of political violence and has been mired in its worst economic crisis in decades.
The device, triggered by a timer and placed in a backpack near the entrance of the Hellenic Business Federation offices, went off around 3:30 a.m. (8:30 p.m. ET) in central Athens, close to parliament in Syntagma Square.
An anonymous caller warned a newspaper some 30 minutes earlier, a police official said on condition of anonymity.
The Cypriot Embassy, across the street from the business federation, bore the brunt of the damage. Police said they had no evidence to indicate the embassy was a target.
"Our embassy absorbed the full impact of the blast. All the exterior windows were blown out and there is incalculable damage to the interior from the ground floor to the sixth floor," Cypriot Ambassador to Athens Kyriakos Kenevezos told media.
Four other buildings were damaged, with glass from smashed windows strewn across the streets.
"I heard it, it made me dizzy because it was so loud," said Kostas Papalogizopoulos, who was working the night shift at a kiosk across the street.
Police cordoned off a two-block area surrounding the building and bomb disposal squads were examining the scene.
Video from a security camera at a nearby building recorded two people wearing dark clothes and helmets leaving the scene on a motorcycle at high speed, a police official told Reuters.
Police were checking other cameras in the area.
Makeshift bomb and arson attacks have escalated in Greece since 2010, when it first adopted unpopular austerity measures such as tax rises, wage and pension cuts in exchange for multi-billion-euro bailouts by the European Union and the IMF.
In July, Athens agreed to further rounds of austerity under its third bailout.
Tsipras' government condemned the attack.
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