Dozens more were injured in the blast which happened at 09:30 on Thursday in the south of the city. The car's driver, who was also killed, has been identified as a 57-year-old man. No group has said it was behind the explosion.
President Ivan Duque described it as a "crazy terrorist act" and declared three days of national mourning.
The grey Nissan Patrol entered the compound of the General Santander police academy where a promotion ceremony for cadets was being held.
When the car was stopped by guards at a checkpoint, the driver accelerated and hit a wall, at which point the car exploded. An explosion of a car bomb of this size is something that has not happened in a long time in Bogotá and so it took the Colombian capital by surprise.
This is all the more so because it happened at a police school, the kind of institution that suffered numerous attacks during the time of drug violence and the armed conflict with Farc and ELN rebels.
Colombian authorities and leaders condemned the "terrorist attack" and said they feared "a return of the bombs". It should be noted that Colombia has significantly reduced bomb attacks and murders in recent years, but what has happened today shows that it is a continuing fear for citizens.
The reaction of the people at peak and Relatives of cadets being trained at the school gathered in front of the gates to find out more information.
President Duque, who was in the west of the country when the explosion happened, returned to the capital and visited the site. "It's an attack on society," he said. "Colombians have never yielded to terrorism, we have always defeated it. This will not be an exception."
Authorities were now investigating who were the "intellectual authors" of the blast, Mr. Martinez said. Among those injured are two Panamanians and an Ecuadorean national.
The explosion was condemned by Colombian politicians, including former Presidents Juan Manuel Santos and Álvaro Uribe, and regional leaders.
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 of the same name.
Peace talks between the ELN and the previous government of Mr. Santos stalled, and President Duque, who takes a more hardline approach to the group, has not resumed the talks.
