Local civil defense officer Luis Fernando Velez said they did not know how many people were still buried under the rubble, but noted that part of the stands was full when it collapsed.
The event was part of the celebrations surrounding the San Pedro Festival, the most popular festival in the region.
“We will ask for an inquiry into the facts of what happened,” Colombia’s outgoing President Ivan Duque said on Twitter, expressing solidarity with the families of the dead and injured.
Orozco said the departmental government would move to ban so-called “corralejas,” in which locals try their luck in the ring, saying they are dangerous and encourage animal cruelty.
On Saturday, several people were injured in accidents in the corralejas in El Espinal, where about 78,000 people live and is about 150 km from the capital Bogota.
Another person died earlier this month after being gored by a bull during a corraleja in the town of Repelon.
President-elect Gustavo Petro, who takes office on August 7, joined Orozco in calling for a ban on amateur bullfights.
While he was mayor of Bogota, the leftist Petro put an end to the bullfights in the city’s signature bullring, La Santamaria.
Although animal cruelty is a crime in Colombia, bullfights and cockfights are protected because of the cultural history behind them.