Many of the victims died as they jumped from the building to escape the flames, a police official said, while witnesses added the death toll could rise.
The cause of the blaze was not immediately clear.
Bangladesh has around 4,500 garment factories that make clothes for brands including Tesco, Wal-Mart, JC Penney, H&M, Marks & Spencer, Kohl's and Carrefour.
Ready made garments make up 80 percent of the country's $24 billion annual exports.
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An ITV News investigation has learned that 99 children were treated on adult mental health wards in the first four months of this year.
Aside from the heat, lightning storms may have kept you awake last night; the Met Office have warned more can be expected tonight.
The temperature is a little cooler, but it's still a very warm day