Officials believe a boiler explosion set off the rapid blaze during a shift change at a packaging factory near the Bangladeshi capital. They fear that some missing workers are trapped in the building.
Police say two other suspected militants were killed in the standoff. They say Tamim Chowdhury, a Bangladeshi-born Canadian, returned to the country in 2013 and supplied guns and arms to militants.
Experts say code used by hackers in recent attacks on banks appears to be the same as code used in an attack on Sony Pictures which the FBI says was carried out by North Korea.
The head of the Society for Worldwide Interbank Financial Telecommunication acknowledged at least two security breaches in addition to February's spectacular theft involving Bangladesh's central bank.
Thieves stole $81 million from Bangladesh's central bank in February using the SWIFT messaging network. Now, a second bank has been attacked in a similar fashion.
Bangladesh has seen a string of attacks against outspoken atheists and secularists, and the government has been accused of not doing enough to protect them.