Most of those killed were women and children, Uganda Red Cross spokeswoman Irene Nakasita said in a statement.
She said at least six people had been rescued and transferred to a nearby hospital, as she posted images of rescuers digging for others.
Kasese district, where the disaster occurred, is prone to landslides, especially during the rainy season, because it sits in the foothills of the Rwenzori mountains that straddle the border with Democratic Republic of Congo.
After a prolonged drought, heavy rains have fallen on much of Uganda since late July, causing deaths and flooding and the destruction of crops, homes and infrastructure.
In July flooding caused by heavy rains killed at least 24 people in Mbale district in eastern Uganda.
The country's weather agency had warned it would be hit by unusually strong and destructive rains in the August-December season and advised people living in mountainous areas to be vigilant or evacuate to safer areas.