The Disaster Management Center announced more than 2,900 people have been displaced.
The military used large armored vehicles and boats to transport people to safe areas. Residents say there are more people trapped in interior villages where boats have been unable to reach, AP reported.
At an intersection close to Agalawatte, 98 kilometers (60 miles) south of capital Colombo, four bodies in coffins were kept in a house, awaiting boats to be taken to a temple where displaced people have taken refuge.
Mudslides have become common during the monsoon in Sri Lanka.