The building housed several garment makers -- including New Wave Style, Ether Tex, Canton Tech Apparel and New Wave Bottoms. The contractors appeal to cost-conscious merchants because of the low wages they can pay Bangladeshi workers.
It was not immediately clear which retailers were doing business with the factories.
A supplier to British retailer Primark was located on the second floor of the building.
"The company is shocked and deeply saddened by this appalling incident at Savar, near Dhaka, and expresses its condolences to all of those involved," Primark said in a statement.
"Primark has been engaged for several years with NGOs and other retailers to review the Bangladeshi industry's approach to factory standards," it said. "Primark will push for this review to also include building integrity."
The last major building collapse in the country occurred in 2005, when more than 70 people were killed in a garment factory collapse in the same area, the Bangladesh Sangbad Sangstha news service reported.
A fire at a clothing factory in a suburb of Dhaka in November killed at least 112 people.
Garments account for 80% of Bangladesh's $24 billion of exports.
The country has about 4,500 garment factories where workers make clothes for brands including Tesco, Walmart, JC Penney, Kohl's and Carrefour.
Scott Nova, executive director of the Worker Rights Consortium, said the disasters keep happening because companies put pressure on factories to lower prices, which results in substandard safety conditions.
"The worse the dangers get, the more business comes in, so the government has no incentive to fix anything," Nova said. "We ask ourselves every day what it's going to take to fix this."