The blast happened outside a school for police cadets in the south of the city.
Thirty-eight people were reportedly injured in the blast which happened at 09:30 local time (14:30 GMT).
Images show a charred vehicle in front of the General Santander school, which is located in a working-class area of Bogotá.
Colombian President Iván Duque, who was in the west of the country at the time of what he said was an "attack", tweeted that he would return to the capital immediately.
He said Colombians would not "bow to violence".
Bogotá's mayor Enrique Peñalosa said he condemned the "terrorist act" but so far the authorities have not said who may be behind the explosion.
Colombian radio station RCN tweeted footage of the scene of the blast.
Car bombs were not uncommon during the decades-long conflict between the Colombian government and left-wing rebels of the Revolutionary Armed Forces of Colombia (Farc).
But local media say there has been no such blast in the past nine years.
The Farc signed a peace agreement with the government in November 2016 and the group has since become a political party.
Another rebel group, the National Liberation Army (ELN), however, is still active.