In Thursday's attack, which the government described as an act of terrorism, the car broke through checkpoints into the grounds of the General Santander School before it detonated, shattering windows of apartments nearby.
Colombian President Ivan Duque said he was returning to the capital from the west of the country, where he had been attending a security meeting and had ordered security forces to find the perpetrators and bring them to justice.
"All Colombians reject terrorism and are united to confront it," he said on Twitter. There was no word on who might be behind the explosion.
Images on social media showed the remains of a vehicle in flames in the parking area of the police school, and emergency responders at the scene.
On the outskirts of the police complex, dozens of family members of the cadets gathered crying and seeking information about what happened to the students hoping to become police officers.
Meanwhile, ambulances were leaving the area with the wounded as helicopters patrolled the skies.
The explosion also broke the windows of several apartment buildings and houses near the establishment. Witnesses told reporters at the site that the vehicle violently entered the police training center before the explosion in which the driver died.
"It's a car bomb that unfortunately violated security filters," Vice President Marta Lucia Ramirez told reporters.