Six fishing trawlers carrying at least 71 boatmen are reportedly missing.
A man and a woman died, hit by falling trees as the cyclone cut its path through the tourist district of Cox's Bazar, police said.
A child died in Bhola, one of the most vulnerable districts in the south. In Rangamati town, trees uprooted by the cyclone fell on a woman and a child, leaving both dead, Police Inspector Mohammad Rashid said.
Separately, in the district town of Cox's Bazar, an elderly woman died from cardiac arrest at a cyclone shelter.
"She panicked at night when the strong winds started," he said quoting family members.
A fisherman fell from his boat and died after the vessel carrying him got caught up in the storm at deep sea, said Kutubdia Upazila Nirbahi Officer Sujon Chowdhury. He was swept away while others in the boat tried in vain to save him, he said quoting the head of the local boat-owners association.
Meanwhile, all efforts to communicate with six missing trawlers carrying 71 men failed to get any results on Tuesday night.
Two of the missing trawlers are from Banshkhali, said Upazila Nirbahi Officer Kazi Md Chahel Tosturi. The vessel carrying eight men went off to fish at sea four days ago, he said.
Four fishing trawlers from Kutubdia carrying 63 men went missing after the storm, said UNO Sujon Chowdhury.
The powerful storm, which prompted authorities to raise the highest level of alert, started crossing the Cox's Bazar-Chittagong coast around 6am with winds speeds of over 100km per hour.
The Met office has said that the cyclone has already started to lose strength, but strong winds and heavy rains in Cox's Bazar and Chittagong may continue throughout the day.
Briefing the media at his office, he said a child has been reported missing during the storm.
Quader said that the government has disbursed cash assistance of Tk 18.7 million for the affected areas. "A navy ship is on its way to the St. Martin's Island with relief supplies. The prime minister has instructed the army and air force to join the relief efforts."