Most of them were killed by falling trees in the districts of Cox's Bazar and Rangamati, BBC reported.
Hundreds of houses were fully or partly damaged, the officials said. Significant damage is reported in refugee camps housing Rohingya Muslims from neighbouring Myanmar.
Cyclone Mora made landfall at 06:00 local time (00:00 GMT) between the fishing port of Cox's Bazar and the city of Chittagong, with winds of up to 117 km/h (73mph), the country's meteorological department said.
Low-lying areas of Cox's Bazar, Chittagong and many other coastal districts were "likely to be inundated" by a storm surge of 1.2m-1.5m (4-5ft) above normal levels, the department had warned.
People have been evacuated to shelters, schools and government offices.
Fishing boats and trawlers have been advised to remain in shelters. Flights in the area have been cancelled.
About 20,000 houses in refugee camps for Rohingya were damaged, community leader Abdus Salam said.
"In some places, almost every shanty home made of tin, bamboo and plastic has been flattened," Mr Salam added. "Some people were injured, but no-one is dead ."