Three people were reported dead in Myanmar as the "extremely severe" cyclone hit Rakhine state in the afternoon, with wind speeds of up to 209kph, the national Meteorological Department said.
The cyclone whipped up heavy rains and wind, destroying homes and displacing several thousand in Myanmar’s port town of Sittwe.
In Bangladesh, the storm destroyed more than 500 Rohingya shelters in Cox's Bazar, officials said.
Nearly 500,000 people were relocated to safer areas in both countries.
The Met Department said the centre of Cyclone Mocha had crossed the Cox's Bazar-North Myanmar coastal area at Sittwe at 3pm local time and was lying over the land area of Myanmar.
"The system is weakening gradually," it said.
Panic in Rohingya camps
Panic gripped the world’s biggest refugee camps in Bangladesh, which hosts 1.2 million persecuted Rohingya refugees, as strong winds and rain uprooted trees and destroyed hundreds of flimsy shelters.
Rains started battering the camps on Sunday morning and weather alerts were raised.
Pictures and videos shared by refugees on social media show makeshift shelters collapsing under strong winds and tarpaulin and bamboo roofs being blown away.
Mohammed Ali, 31, of Nayapara refugee camp, told The National: “My house is shaking as though it will fall any time. They are so flimsy as it is made of bamboo and will collapse any time.
“My children are scared but we have nowhere to go.”
Rohingya refugees who fled genocide in Myanmar in 2017 are not allowed to build permanent structures using brick and mortar. The host government also does not allow them to leave the camps, leaving many exposed to the threat posed by the cyclone.
Though Myanmar and Bangladesh relocated thousands of families from low-lying areas before the storm, there are no cyclone shelters in Cox’s Bazar, the world’s biggest refugee settlement.
Many people took shelter in schools, learning centres and women’s refuges run by international agencies in Cox’s Bazar.
Jameela, 23, a mother of two, said she had taken shelter in a school near her camp in the Teknaf area, to stay safe from the deadliest storm to hit Bangladesh in the past two decades.
“We are currently staying in a school and it is packed with families,” she told The National.
“My house is not liveable any more. The roof blew away and it is badly damaged.
“I don’t know for how long we have to live here. I am just relieved that we are getting food and water for the kids.”
Alom Bin Nur, a Rohingya from the Balukhali camp, told The National he and his family had moved to a neighbour’s house after the roof of their shelter collapsed.
“They are a local family and we have to stay the night with them to protect us from the rain and storm. But now the wind has reduced, we are back in the shelter and have started cleaning and some repairing work.”
Hundreds of Rohingya shelters destroyed
Mohammed Mizanur Rahman, Bangladesh's refugee, relief and repatriation commissioner, told The National that the impact of the cyclone was "not as bad as expected".
"But the rain and the wind speed impacted the refugee settlements. Our initial estimation is that 500-plus shelters have been damaged," said the official.
One of the biggest fears is the aftermath of the cyclone will trigger a deluge of rain that will cause flooding and landslides in the camps.
"We are hoping that the rain will subside by this evening," said Mr Rahman. "Then we are looking at a much better situation. we expect that people can return to their homes within two days."
Rohingya volunteers in action
As the heavy rain and storm started wreaking havoc, camp leaders and trained Rohingya volunteers from the Disaster Management Unit sprang into action to help rebuild shelters and distribute food, medicine and other emergency support to affected communities.
A Majhi, or camp leader, at the Kutupalong refugee site, told The National several shelters had been crushed under uprooted trees.
“Our camp is surrounded by big trees, many of which got uprooted in the wind. Maximum damage so far is caused by falling trees,” he said, adding that there had been no casualties in the camp.
“We have relocated some very small number of families to the learning centre for their safety.”
International agencies including the UN High Commission for Refugees (UNHCR), International Organisation for Migration (IOM) and Bangladeshi government agencies put together an emergency response plan to mitigate the risks posed by the cyclone.
Johannes Van Der Klaauw, UNHCR spokesman in Bangladesh, told The National his organisation, together with local authorities and humanitarian partners, was responding to urgent needs on the ground.
"We have pre-positioned emergency shelter materials and aid agencies are on standby to provide 250 tonnes of dry food and 50,000 daily meals if needed," he said.