The 300ft-high (91m) pile of rotting debris had shifted after floods and a fire then collapsed on Friday.
At least 40 homes on the edge of the dump were destroyed. The army said an unknown number of people were missing.
There had been concerns over the safety of the site in Colombo, with residents demanding it be cleared.
The AFP news agency said about 800 tonnes of waste were added to the Meethotamulla dump every day, and that the government had planned to remove it.
"We heard a massive sound. It was like thunder," one resident, Kularathna, told the Reuters news agency. "Tiles in our house got cracked. Black water started coming in."
The collapse occurred as many people were marking Aluth Avurudda, or the Sinhalese New Year, a major public holiday across Sri Lanka.
Emergency officials told the BBC that up to 20 people may remain buried in their houses, with the Sri Lankan army now co-ordinating the recovery.
One disaster emergency official told AFP the death toll would have been higher had many people not left their homes after the fire at the dump, hours before the collapse.
One government minister, Harsha De Silva, said in a statement that no more rubbish would be dumped at the site, and would instead be placed in two other sites.
It is not clear when the decision is made. Footage filmed by the BBC on Saturday showed people continuing to dump rubbish at Meethotamulla.
Mr De Silva said residents had been advised to leave because of the risk of landslides.
"It's unfortunate that even though payments had been made for those families under risk of landslides to move out some had not done so. They had even been advised to leave as recently as two days ago," he said.
Last month, a landslide at a rubbish dump in the Ethiopian capital, Addis Ababa, killed at least 113 people.
At least 19 people, including five children, have died after a huge rubbish dump collapsed on to their homes in Sri Lanka, the army says.