The explosion happened near the city's bullring, where animal rights activists were preparing to hold a march in protest at a decision to reinstate bull-fighting in the city.
Many of the injured are believed to be officers who were deployed to the area ahead of the protest, the mayor's office confirmed. There are unconfirmed reports that a policeman has been killed in the explosion.
Bogota mayor Enrique Penalosa, who attended the scene, said he was convening a security council meeting for Sunday (19 February) afternoon.
"The terrorists won't intimidate us," Mayor Penalosa said on Twitter. "We are going to do all that's necessary to capture them."
Eyewitnesses described chaotic scenes in the aftermath of the explosion. Gareth Lewis, a British traveller staying in a hostel in La Macarena, close to where the blast occurred told the BBC: "I was sitting in my room in the hostel, the windows just came in, there was glass everywhere.
"Quite a few police have been hurt, they're now sweeping up. They used tear gas and there's quite a bit of blood."
The area has been the focus of protests by animal rights activists in recent weeks after a constitutional court passed a ruling to reinstate the blood-sport, declaring it a part of the country's heritage.
Bullfighting was banned in 2012 by the capital's mayor at the time, Gustav Petro. But Columbia's Constitutional Court overruled the ban in 2014, arguing that it violated bullfighters' rights to freedom of artistic expression.
Animal rights campaigners have been staging demonstrations since the reopening of the bullring resulting in violent clashes with police.
In January, officers were forced to use tear gas to disperse protesters who were reportedly attacking spectators.
Bullfighting is banned in several Latin American countries, including Argentina and Uruguay. The sport is also prohibited in Cuba and in several Mexican states.