There were no injuries, police said.
Eurobank is Greece's third-largest lender by assets.
Small-scale attacks on businesses, police and politicians are frequent in Greece, which has a long history of political violence and is still struggling to emerge from a crippling debt crisis.
Eight 'suspect' packages found at Athens postal centre
"The explosion damaged the entrance and smashed some windows," a police official said, adding that some nearby buildings were also slightly damaged.
Police had cordoned off most streets in the surrounding area following a warning call to a local news website. The explosion, which occurred at 2238 local time (1938 GMT), was loud and was heard in central Athens.
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