The fire was reported at about 1 a.m. at the bank, located at 464 California St.
A window on the front of the building was broken and newspapers were set ablaze inside underneath the windowsill, according to police.
The blaze is considered suspicious but no suspect information was immediately available this morning, police said.
Anyone with information about the fire is encouraged to call the Police Department's anonymous tip line at (415) 575-4444 or send a tip by text message to TIP411.
