Hours of heavy rains overnight caused rivers to burst their banks, flooding homes with mud in Putumayo province.
An unknown number of people are missing. One army officer said the main local hospital was struggling to cope.
President Juan Manuel Santos, who is travelling to the area, said troops had been deployed as part of a national emergency response.
The region's governor, Sorrel Aroca, told Colombian media that whole neighbourhoods had been buried.
Jose Antonio Sanchez, mayor of the provincial capital Mocoa, told Caracol radio that the town was "totally isolated", without electricity and water.
President Santos said, on Twitter, that he was taking charge of the situation and that Colombians were in mourning for the victims.
A representative of the National Disaster Risk Management Unit told AFP news agency that the mudslides were caused by the rise of the Mocoa River and three tributaries.
March was the country's rainiest month since 2011, according to the state meteorological agency.
Putumayo borders Ecuador and Peru.
Across Peru more than 90 people have died since the start of the year because of unusually heavy rainfall, which also caused landslides and flash floods.
Source : BBC
