Many more people are feared trapped after building collapse and frantic efforts are under way to rescue those beneath the debris.
The army is helping with the rescue operation on the outskirts of Dhaka.
Building collapses are common in Bangladesh where many multi-storey blocks are built in violation of rules.
The eight-storey building contained a clothing factory, a bank and several other shops. It collapsed during the morning rush hour.
Many people have gathered near the scene looking for friends and relatives.
It is not yet clear what caused the collapse but local media reports said a crack was detected in the block on Tuesday.
Rescue workers are using concrete cutters and cranes to dig through the rubble.
Local police chief Mohammad Asaduzzaman told the Reuters news agency that factory owners appeared to have ignored a warning not to allow their workers into the building after the crack was detected.
Police told local media that the rear of the building suddenly started to collapse on Wednesday morning and within a short time the whole structure – except the main pillar and parts of the front wall – had caved-in, triggering panic.
Only the ground floor of the Rana Plaza in Sava remained intact after the collapse, officials said, as army and fire service rescuers equipped with concrete cutters and cranes dug through rubble to pull out trapped people. Many onlookers also joined the effort using their bare hands.
Survivors have described their terror as the collapse began.
“I was in the cutting section of the garment factory and suddenly we heard a huge noise and the building collapsed within a few minutes,” a garment worker told private Somoy TV.
“I removed the rubble and came out with two other workers. But at least 30 other workers in my cutting section were still unaccounted for,” he said.
In November, a fire at a garment factory in a Dhaka suburb killed at least 110 people and triggered a public outcry about safety standards in the industry.
The last major building collapse was in 2010, when a four-storey building collapsed in Dhaka killing at least 25 people and injuring several others.
Bangladesh has one of the largest garment industries in the world, providing competitively priced clothes for major Western retailers which benefit from its widespread low-cost labor.
Following November’s fire, Western retail chains who buy from factories in Bangladesh urged factory owners to improve safety standards.
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