An anonymous caller gave a warning in a call to the Zougla website and police were able to close off the area before the explosion, the source added.
The device was placed in a bag close to the bank's entrance, exploded at around 1930 GMT, 35 minutes after the warning was given causing damage to the bank and surrounding buildings.
Non-lethal attacks on economic, political and diplomatic targets, blamed by police on extreme left or anarchist groups, have been common in Greece for years.
They are often claimed on behalf of groups representing such movements despite the arrest and sentencing to heavy prison terms of many activists.
In April 2014, the Bank of Greece was targeted in a blast claimed by anarchist group Revolutionary Struggle.
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