No group claimed responsibility for the 6 a.M. (local time) explosion, which shattered windows in the central bank branch and buildings up to 200 metres away, and left the charred remnants of a car with only two wheels recognisable.
The attack hit a largely commercial zone with a large shopping mall and banks, a few blocks from the Greek parliament.
It came one day ahead of a visit to Athens by German Chancellor Angela Merkel, whose country is the largest single contributor to Greece's bailout programme.
Forensic experts began combing through the blast site, while gaggles of office workers unable to get to their offices gathered in nearby cafes.
More From This Section
An officer said the size and composition of the bomb were still unclear, and the anti-terrorism squad was taking over the case. He spoke on condition of anonymity, as the investigation is still at a very early stage.
The news website that received one of the anonymous calls said the caller warned a bomb containing 75 kilogrammes of explosives had been planted in a car.
The government has hailed the return to the bond market as proof that the country is emerging from its deep financial crisis.
"The evident target of the attackers is to change this image, and change the agenda," government spokesman Simos Kedikoglou said on an early morning television news show. "We will not allow the attackers to achieve their aim."
Greece has a long history of domestic militant groups who plant usually small bombs late at night that rarely cause injuries.