The 300ft-high (91m) pile had shifted after floods and a fire, and subsequently collapsed on Friday.
At least 40 homes on the edge of the dump were destroyed, with four children aged between 11 and 15 killed.
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.
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.
Last month, a landslide at a rubbish dump in the Ethiopian capital, Addis Ababa, killed at least 113 people.