Rising water levels caused mudslides which swept away homes in Quetame, a municipality south-east of the capital, Bogotá.
Rescue workers are searching for at least a dozen people who have been reported missing.
A bridge linking Bogotá with the city of Villavicencio has been destroyed.
Among those killed are three children aged 12, 10 and six, rescue workers said.
The 12-year-old was swept away by a mudslide along with his mother, newspaper El Tiempo reports.
Colombian President Gustavo Petro expressed his condolences on Twitter.