The blasts occurred in the west of the city, in front of the office of the attorney-general - the country's top prosecutor - and not far from the US embassy.
An official told the Associated Press news agency that "terrorists" were responsible, but did not specify which group was suspected.
Colombian President Alvaro Uribe has vowed to fight the Marxist rebels who control some 40% of the country, as well as right-wing paramilitaries and the drug trade armed groups thrive on.
Local television said the bombs were planted by two men on a motorcycle - but this has not been confirmed.
There was no damage to the attorney-general's office.
Drug wars
In October, police raided shanty towns in Bogota, after a car bomb attack outside police headquarters killed two people and injured almost 40.
Police at the time blamed the main leftist rebel group, the Revolutionary Armed Forces of Colombia (FARC).
Previously, the city had been spared the worst of Colombia's four-decade war.
Since taking office in August, President Uribe has introduced a series of tough new measures to pursue the rebels, some of which entail the suspension of basic civil liberties.
They include the establishment of a civilian spy network and paid informers, arms for peasants in vulnerable parts of the country, and the detention of suspects without warrants and imposition of curfews in certain zones.