"A twister accompanied by a hail storm flattened more than 3,000 houses in Northern Gaibandha district, killing at least 12 (people)" late on Sunday night, district police chief Bhanu Lal Das told AFP.
"The death figures will go up as we cannot start full-scale search operations because of the rough weather," he added.
Winds of about 100 kilometres per hour (62 miles per hour) destroyed crops, uprooted trees and electricity poles, cutting off communications to the 15 villages, in one of the most impoverished parts of the country.
"We suspect more bodies are stuck up in the flattened houses," Das said, adding the hail storm and continuous downpour made search operation difficult.
More than 200 injured people were rushed to different hospitals and clinics in the district, police said.
Tropical storms frequently hit Bangladesh during summer. Before Sunday's storm, at least 20 people had been killed in five tropical storms in different Bangladesh districts since earlier this month.