Cartagena mayor Antonio Cartagene said the man was carrying an AR-15 rifle.
The gunman, a man in his 20s, was shot in the head by a police officer.
“We do not understand what happened.
I do not know,” Cartagenas office said in a statement.
“The situation was under control and there were no witnesses.”
The man who died on the sidewalk was identified as Miguel Rodriguez, a 34-year-old who was visiting Cartageno.
The shooting occurred on the plaza near the city’s international airport.
“We’re going to ask the mayor of Cartagenos government to take the necessary measures to calm the situation,” Cartas office added.
“Please pray for us, and please pray for the family of the victim.”
A video posted on YouTube on Saturday showed a small crowd gathered on the edge of the street, holding signs that read “Free the Martyrs” and “Don’t Shoot.”
The mayor also called for calm on Sunday.
“Our priority is the safety of our citizens and the families of the martyrs, as well as the city of Cartags residents,” he said.