"We suspect it is linked to terrorism," said a police official who declined to be named.
The medium-sized device was planted underneath the bank's ATM machine, police said, adding that there had been no warning call and no one claimed responsibility for the blast.
Arson attacks against banks, foreign firms and local politicians have become more frequent in Greece in recent years as the country battles soaring unemployment and struggles through a recession deepened by austerity policies imposed by foreign lenders. They are usually blamed on far-left groups.
In June, gunmen rammed a van packed with gas canisters into Microsoft's Greek headquarters in Athens and then set the vehicle on fire. A fringe leftist militant group claimed responsibility for that attack.