The explosions on Wednesday occurred near ATM machines in branches belonging to Citibank and Banco Galicia, damaging the building's facades, officials said.
The blasts occurred before the banks opened. A 38-year-old security guard was killed at a Citibank branch in downtown Buenos Aires.
Hernan Fernandez, a spokesman for a private ambulance service, confirmed the fatality. Police also they also deactivated two explosive devices and at least one officer was injured.
No group immediately claimed responsibility for the bombings.
Banks remain a flashpoint of public anger following Argentina's 2001-2 economic crisis.
Billions of dollars in bank accounts held by Argentines were frozen as the government tried to thwart a run on the banks and prop up a tottering financial system.
Since then, hundreds of thousands of people have filed lawsuits hoping to recover their savings, much of which were forcibly converted from dollars to devalued Argentine pesos.