Thirteen people have so far been pulled out of the ruins alive, this according to officials.
Some 45 people, including construction workers, residents and children from a Koranic school, are missing.
Witnesses say the 12-floor building under construction is now a "huge pile of chaos".
"I thought there was an earthquake and then I heard screaming. The whole building fell on itself," eyewitness Musa Mohamed told the AFP news agency.
A huge crane is being used to pull out a mass of iron bars so as to access the centre of the building, where some people are thought to be still alive.
Bulldozers are also being used to move the rubble.
Trapped victims are said to be making phone calls to friends and relatives
Large crowds of onlookers, as well as rescue workers and armed police officers have gathered at the scene.
The collapsed building was near a mosque, as well as other residential and commercial properties in central Dar es Salaam.
By Jane Gakaria
Source: BBC News.