President Juan Manuel Santos said the former minister, Fernando Londono, was hurt but was out of danger.
Santos said in a brief televised declaration that Londono's driver and a police escort were killed in the bombing, which occurred just before midday on Calle 74 a half block from Caracas Avenue.
Londono had been riding in an armoured SUV and TV images showed him being escorted, walking but stunned, from the vehicle in a suit and tie with blood stains on part of his chest. One of his bodyguards holds a gun.
"Fortunately, Dr. Londono is stable. He's in the hospital," said Santos.
Neither the president nor police offered more details or ascribed blame for the attack.
City health director Guillermo Jaramillo told Caracol Radio that at least 19 people were hurt.
Earlier Tuesday, police said they had deactivated a car bomb in the centre of the city that they said they presumed was from the Revolutionary Armed Forces of Colombia, the country's main leftist rebel group, known as the FARC.
Londono was interior minister from 2002-2003 under former President Alvaro Uribe and is an outspoken conservative foe of the FARC.