The collapse happened at around 3 a.m. (0100 GMT) in the impoverished Hulene neighborhood, which is around 10 kilometers from the center of Maputo. The houses were built illegally and authorities had previously asked the residents to leave, officials said.
Torrential rain is thought to have caused the loose waste to shift and crash down on the shacks, trapping the occupants who were sleeping at the time of the incident on Sunday night.
Mozambique's emergency service warned there could be more victims, trapped under the vast waste pile in Hulene.
"The information we received from local authorities is that the number of people living in those houses exceeds the number of deaths recorded, so work is still ongoing to see if there are any other deaths," said spokesman Leonilde Pelembe.
The rubbish mound destroyed five homes and rescue teams were still searching through the wreckage to find survivors, he added.
"I live in this neighborhood because I have nowhere to go. Had the government told me to go to another place to live, I would have left here," said local resident Maria Huo.
Her family home was partially destroyed and her son injured in the landslide, she said.
"It's been more than 10 years that the dump should have been closed because it's full -- but they still continue to pile trash on the trash. The consequence is this," said Teresa Mangue, a neighborhood leader.
Heavy rain has been falling on Maputo since Sunday, causing flooding, damaging homes and deluging roads and schools.