The number of people trapped was unclear, but several people have told local media that they have lost contact with relatives who they believe were inside the building, AP reported.
More than 80 people have been rescued from the four-story building, which housed dozens of shops and collapsed Saturday morning.
Tanzanian President Samia Suluhu said on Sunday that more than 20 people were receiving medical treatment and the government would cover the costs.
She ordered an audit of all buildings in Dar Es Salaam's Kariakoo area, which is popular among traders, and asked police to obtain the ownership and construction permits for the collapsed building.
Some of those who died were being buried on Monday.
It is currently the rainy season, when building collapses are common in the east African country. Buildings that collapse are often found to have violated construction regulations.