AFP reports citing rescue officials.
Only the ground floor of the Rana Plaza in the Savar district, which also housed a garment factory, remained intact, said the officials.
"We have recovered three bodies, two of them were women," said Abul Bashar, an official in the fire service. "Many people are feared dead," he told AFP, adding that the military has been called in to help the rescue effort.
A source at the nearby Enam Medical College told AFP that at least 35 people had been admitted to the hospital with injuries. A further 150 people, most of them garment workers, had received first aid at the hospital without being formally admitted.
Local police chief M. Asaduzzaman told AFP that the situation was "disastrous and at least 100 people are feared trapped".
Building collapses are common in impoverished Bangladesh as most defy the government's construction code to construct multi-storey buildings.
More than 70 people were killed after a multi-storey garment factory collapsed in the same area in 2005. In November at least 13 people were killed after an under-constructed flyover broke down in the port city of Chittagong.