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.
More top news
Low pressure remaining in control gives more unsettled weather for the UK this weekend.
Charlie Gard, the baby boy whose fight for life captured the attention of the world has died, his family has confirmed.
A Royal Marine who lived a "dangerous double life" as a terrorist bomb-maker claims he faked Irish Republican sympathies out of fear.