The blast damaged the office block housing Caracol Radio, blowing out the windows of nearby buildings and cars.
It was not clear if the radio station was the target of the explosion, which left at least nine people injured.
President Juan Manuel Santos, who took office at the weekend, described the blast as a "cowardly terrorist act".
"Their only aim is to sow fear and that they will not achieve," he told reporters after visiting the scene on Thursday morning. "We will continue to fight terrorism."
Television pictures showed a bus with shattered windows and panicked residents in the streets following the explosion, which happened at around 0530 (1130 GMT), as the Caracol Radio morning show began.
The radio programme continued from the 12-storey building despite the explosion.
Caracol Radio's Dario Arizmendi described seeing ceiling tiles fall down as he was live on on air.
Local resident Julian Wilches told the BBC: "We were woken up by a shockwave and thought it was a tremor."
"All our windows are broken – a neighbour on the 12th floor claims a piece of a car made it to her apartment."
The head of the Colombian National Police, Gen Oscar Naranjo, appealed for calm while investigations were carried out.
Bogota's police chief, Gen Cesar Pinzon, blamed leftist rebels for the car bomb, but added that officers were not yet sure if the bomb was aimed at the radio station or at several nearby bank headquarters, the Associated Press reported.
Bomb attacks on Colombian cities decreased under Mr Santos's predecessor, Alvaro Uribe, who was president from 2002 until 7 August this year.
Mr Uribe pursued a hardline stance against left-wing guerrilla groups such as the Revolutionary Armed Forces of Colombia (Farc), which has been fighting the Colombian government since the 1960s.
Source: BBC News