Several foreigners are said to be among those taken by gunmen, who stormed a restaurant in the capital Dhaka
One kitchen staffer said that the gunmen were armed with firearms and bombs, entering the bakery at around 9:20pm local time and taking customers and staff hostage at gunpoint.
Bangladesh's police chief has confirmed that several foreigners are among the hostages.
At least two policemen are reported to have been killed as officers surrounded the restaurant, located in the Gulshan area of the capital, and a massive firefight erupted.
Another 25 officers and one civilian are being treated for injuries, with 10 people in a critical condition, according to hospital authorities.
The jihadist news agency Amaq have reported that the so-called Islamic State are claiming responsibility for attack.
A large number of security guards have cordoned off the surrounding area.
A police spokesman said: "Our first priority is to save the lives of the people trapped inside."
The head of Bangladesh's elite security force told reporters: "We are trying to communicate with them (gunmen). We want to resolve it peacefully."
A resident near the scene of the assault said that gunfire could still be heard almost three hours after the attack began.
"It is chaos out there. The streets are blocked. There are dozens of police commandos," said Tarique Mir.
One Bangladeshi TV station has reported that the gunmen chanted "Allahu Akbar" as they launched their assault.
The restaurant is located near a small hospital as well as the Nordic Club, a private members' club popular with expats.
The US State Department has said the hostage situation is "still fluid", and the US embassy in Dhaka has urged citizens to shelter in place.
A spokesman for the US State Department said it was too early to say who was involved in the hostage situation, but that all Americans working at the US mission in Dhaka had been accounted for.