Calls to two Greek newspapers at 0050 GMT -- 40 minutes before the explosion -- had forewarned police of the attack against the Hellenic Federation of Enterprises (SEV), enabling them to clear the area, the source said.
"The bomb will explode in 40 minutes. This is not a hoax," the caller said, according to news reports.
The police quickly discounted a possible jihadi connection, pointing out that the warning before the attack and the target chosen indicated it was likely a far-left domestic group.
The authorities say they have tightened security following the November 13 attacks in Paris claimed by the Islamic State group.
Television footage showed smashed windows on the building, which is next to one of Athens' top hotels and near the embassy of Cyprus.
State TV also broadcast pictures of the hotel's lobby, showing broken windows and pieces of plaster on the floor.
Offices belonging to the European Union are just around the corner.
State TV said hotel rooms overlooking the street were briefly evacuated.
According to reports, the bomb had been placed in a backpack outside the association's offices, situated near central Syntagma Square.
The assailants set on fire a cannister of gasoline outside the home of minister of state Alekos Flambouraris, a close aide of Prime Minister Alexis Tsipras.
"Politicians, you have no reason to sleep peacefully," said an message posted on an anti-establishment website yesterday in relation to the arson attack, which blackened the front door.
Tsipras' leftist government in July agreed to an unpopular EU bailout to prevent Greece being ejected from the euro.
The government has been forced to legislate new spending cuts and is about to overhaul Greece's pension system, with a possibility of introducing higher contributions.
The SEV offices had been targeted in an arson attack in 2010 claimed by a far-left group named Zero Tolerance.
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