Police officer Asharaful Alam said the explosion occurred on Saturday afternoon at the plant of Sima Oxygen Limited near the port city of Chattogram (Chittagong), 250km southeast of the capital Dhaka, killing five plant workers.
The sixth man died as a large piece of metal fell onto his shop near to the site of the blast that also caused a fire, he said.
It took nine fire engines more than one hour to douse the flames while firefighters also rescued those who were injured at the site of the blast, Alam said.
The blast ripped through the metal structures of the factory, causing extensive damage to the plant that produced oxygen for industrial use, mostly for the shipbreaking industry in Chattogram, the officer added.
Shamim Ahsan, chief of Chattogram Medical College Hospital, said 21 people were being treated at his facility.
Four others were being treated at other hospitals, he added.
It was not immediately clear what caused the explosion.
The government has launched an investigation into the blast and has asked a three-member panel to report back in a week, Abul Bashar Mohammed Fakhruzzaman said.
Deaths from fires and blasts at industrial production sites are a frequent occurrence in Bangladesh.
Nearly 50 people died when a blast triggered a massive fire at an inland container depot in Chattogram in June last year.