A number of makeshift houses are now buried under tonnes of waste.
The area has been a dumping ground for Addis Ababa’s rubbish for more than five decades.
Local resident Tebeju Asres told the AP news agency that the family’s house had been swallowed by the landslide.
“My mother and three of my sisters were there when the landslide happened. Now I don’t know the fate of all of them.”
Many people had been scavenging at the site to make a living, and some even resided there permanently.
There are fears that the death toll will rise further.
The authorities have been building Africa’s first waste-to-energy plant near the landfill.
They plan to burn rubbish generated by the capital’s estimated four million people and convert it into electricity.
Source: BBC UK