Local chief government administrator Tofayel Ahmed said the Upaban Express train was heading for the capital, Dhaka, when the crash occurred around midnight at Kulaura in Moulvibazar district on Sunday.
He said the rail bridge broke down when the train was crossing it. The cause of the breakdown wasn't known immediately, AP reported.
Ahmed said at least 15 passengers were in critical condition. The bodies of three women and a child were kept in a local health complex, he said.
Local TV stations said more than 100 people were injured.
Another official Mesbah Uddin Ahmed said engineers and workers were working to retrieve the coaches while the search for any people trapped under the wreckage was continuing.
The train service between the northeastern region and the rest of the country was halted.