Vice President Francia Marquez said the incident occurred on Friday in an area inhabited by indigenous people.
Most of the 33 victims are children.
The governor's office said that the authorities temporarily closed the road linking the cities of Medellin and Quibdo due to damage caused by several landslides after large amounts of rain fell in Chocó province during the past 24 hours.
Previously, it was believed that about thirty people were trapped under the mud blocks. In footage broadcast on social media and television, the earth could be seen rushing from the mountainside onto the road, burying cars.
According to the disaster management, thirty-five wounded were taken to hospital. A local leader said that many were able to get out of their cars and flee to a house near the town of Carmen de Atrato, to be buried there by another landslide.
Police said they were working with rescuers and disaster management in the rescue operation. About fifty soldiers also arrived at the scene to participate in the search for the missing people.
President Gustavo Petro promised all available assistance to the province of X-en Chocó.
