According to reports by Reuters news agency, the collapse was due to heavy rain. The collapse buried seven houses, officials said.
The collapse happened at around 1am GMT in the impoverished Hulene neighbourhood, which is around 6 miles from the centre of Maputo.
The houses were built illegally and officials said authorities had previously asked the residents to leave.
“Up to now 17 dead bodies were recovered,” a councillor for Ka Mavota Municipal District, Despedida Rita, told reporters. “We fear more might be unaccounted for. So we will keep searching for bodies buried underneath the garbage pile.”
A spokesman for the emergency services, Leonilde Pelembe, said it was likely there were more victims under the waste, according to BBC News.
“The information we received from local authorities is that the number of people living in those houses exceeds the number of deaths recorded,” Mr Pelembe said.
Land pressure in many African cities leads some people to squat on land they do not own as they seek higher wages available in urban centres, according to Reuters reports. The dwellings are sometimes built on land that is marginal or unsafe.
[UPDATE 21 February]
Around 80 families still living in the vicinity of the waste dump are being moved to temporary accommodation in another nieghbourhood of the city, Minister of State Administration Carmelita Namashalua told BBC News.
She said the move was necessary because they could be at risk if there is any further collapse.
The government says search and rescue efforts will continue at the rubbish site until all survivors and missing people are accounted for.
BBC News has reported that a two-year-old child is among the 17 victims.