Video shows the moment when wooden stands collapsed at the makeshift stadium at El Espinal in Tolima, where the annual San Juan and San Pedro festivities were underway.
The incident took place during a “corraleja”, an event where members of the public jump into the ring to run alongside the bulls.
At least one bull is reported to have fled the stadium to adjacent streets.
“At this point we have confirmed four (dead) victims – two women, an adult male and a minor – plus about 30 people seriously injured,” Governor Ricardo Orozco told BluRadio Colombia, a local radio station.
“Of course we have activated all the hospitals and ambulances that we can work with.”
It is feared that the actual number of injured could be much higher.
When news of the incident became known, Major Luis Fernando Vélez, director of the civil defense department, told a local radio station that “500 injured have been reported”.
A statement from Espinal’s mayor’s office said they are “deeply sorry for what happened in the arena”.
“We want to call on the entire community to calm down,” it continued.
“When the emergency became known, aid organizations immediately sprang into action and evacuated the injured for primary care at San Rafael Hospital in the municipality.”
But according to a local news report, a city councilor said hospitals cannot handle the influx of patients.
“We need help from ambulances and neighboring hospitals, many people are still unattended,” Iván Ferney Rojas told El Tiempo newspaper.
Sunday’s event has put bullfighting in the spotlight, with Columbia president-elect Gustavo Petro calling for similar shows to be halted.
“This had happened before in Sincelejo,” he tweeted.
“I ask the mayors not to authorize more shows involving the death of people or animals.”