Thousands have moved to shelters in Bangladesh but in Burma, authorities have encountered a deep reluctance to move among Rohingya refugees |
The storm hit Patuakhali district on Thursday with winds of up to 100km/h (60mph), and was heading for the ports of Chittagong and Cox's Bazar.
At least two people have been killed, Bangladeshi officials say.
Hundreds of thousands of people have been ordered to evacuate low-lying areas in Bangladesh and Burma, and take shelter in cyclone centres.
However, some displaced people in Burma have resisted calls for them to evacuate camps in Rakhine state.
The United Nations has warned that 8.2m people could be at risk from Mahasen in Bangladesh, Burma and north-east India.
Centres crowded
The Bangladeshi authorities have raised the danger level to seven out of 10 for low-lying areas around Chittagong and Cox's Bazar.
The cyclone covered more than 175km in nine hours before hitting Bangladesh, the country's Meteorological Department said.
However, the service's deputy director, Shamsuddun Ahmed, told AFP news agency the cyclone was not expected to cause serious damage as it was "not severe".
The cyclone "did not gain strength in the last part of its journey as it hit the coast", he said.
In Bangladesh, there have been reports of waist-deep water submerging low-lying areas and houses being damaged. Dozens of huts collapsed when the cyclone struck Patuakhali district, eye witnesses told local media.
There are also fears of a storm sea surge.
All schools, colleges and some hotels have been declared cyclone shelters, the BBC's Mir Sabbir reports from Dhaka. These centres are crowded and people are still rushing in, our correspondent adds.
Airports in Cox's Bazar and Chittagong have been shut until the danger subsides.
Authorities warned that heavy rainfall could cause landslides in the hilly regions around Chittagong.
In Burma, meanwhile, tens of thousands of Rohingya Muslims living in camps in low-lying areas of Rakhine state are feared to be at risk.
They were displaced by ethnic violence last year and many are reluctant to move from the camps.
Hla Maung said he lost his mother and two young daughters during the clashes between Muslims and Buddhists.
"I lost everything. I don't want to go anywhere. I'll stay here. If I die, I want to die here," he said.
Rakhine state said it had moved some 36,000 internally displaced people (IDPs) from camps, Kirsten Mildren, from the UN Office for the Co-ordination of Humanitarian Affairs (Ocha), told the BBC.
But she said the evacuation was "not moving as fast as we'd like - it's certainly a race against time. We're finding it very difficult to convince [people] to move to higher ground or safer buildings".
Burmese planning minister Tin Naing Thein said that in all more than 166,000 people had been relocated, but there was little evidence of a mass evacuation in reports from the affected area.
Correspondents say the Burmese evacuations are seen as a test of the government's resolve to assist the Rohingya, amid allegations that state forces stood by or even participated in last year's anti-Muslim violence.
On Tuesday, President Thein Sein was quoted as urging officials to "carry out relief work on humanitarian grounds for all, regardless of race and religion", at a meeting to co-ordinate relief efforts for Cyclone Mahasen.
Cyclone Mahasen has already taken a toll. Though the storm did not make landfall in Sri Lanka, the associated heavy rain caused floods and mudslides which killed at least seven people, according to the country's Disaster Management Centre.
At least 50 Rohingya Muslims drowned on Tuesday when boats evacuating them from the path of the cyclone capsized off western Burma.
Credit & Copy From; http://www.bbc.co.uk/news/world-asia-22537615