It was caused by a percussion bomb designed to cause panic through a loud noise but cause limited damage, he said on condition of anonymity because civil servants are barred by law from speaking to journalists without prior authorization.
The person's injury was not life threatening, the official said.
NTV, a private television station, said the bomb was placed in a trash can outside the bank.
There have been several bomb attacks on the streets of Istanbul this year, all blamed by the government on Kurdish rebels fighting for autonomy in southeastern Turkey.
But leftist groups also frequently attack bank branches across the country.
