The cyclone is gaining power and has grown to a category four storm with wind speeds reaching 240 km (150 miles) per hour, which could lead to tidal waves up to 7.5 meters (25 feet) hitting the coast.
The engineer said the authorities were doing their best to minimize any potential damage.
"The evacuation of people from coastal and low-lying areas to temporary camps is almost complete," he said.
Mongla and Chittagong, the country's main ports, have suspended work, and Chittagong international airport has been closed. The police are being aided by the military in assistance operations.
The cyclone may also affect eastern India and the west coast of Myanmar, where officials are likewise evacuating people from coastal areas.
Cyclones kill hundreds of people in Bangladesh annually. However, following devastating cyclones in 1970 and 1991, which claimed half a million and 140,000 lives respectively, the south Asian country introduced a better storm warning system and built some shelters.