Cyclone Mocha began to crash ashore at the Bangladesh-Myanmar border on Sunday, Bangladesh's weather office said.
Packing winds of up to 195 kilometres (120 miles) per hour Mocha hit between Cox's Bazar and Myanmar's Sittwe, the office said.
The US Joint Typhoon Warning Center earlier said Mocha was packing winds up to 140 knots, or 259 kph, equivalent to a category 5 hurricane on the Saffir-Simpson Hurricane Wind Scale.
"The wind is getting stronger at the moment," rescue worker Kyaw Kyaw Khaing told AFP earlier from Myanmar's Pauktaw, about 25 kilometres inland from Sittwe, and where he said around 3,000 people had arrived to seek shelter.
"We distributed enough food for one or two meals to the people evacuated to temporary shelters. I don't think we will be able to send any food today due to the weather."
Thousands left Sittwe on Saturday, packing into trucks, cars and tuk-tuks and heading for higher ground inland as meteorologists warned of a storm surge of up to 3.5 metres (11 feet).
A media account run by junta authorities in Rakhine showed what it said were trees downed over a road near Sittwe.
"We are not OK because we didn't bring food and other things to cook," said Maung Win, 57, who spent the night in a shelter in Kyauktaw town. "We can only wait to get food from people's donations."
Bangladeshi authorities moved 190,000 people in Cox's Bazar and nearly 100,000 in Chittagong to safety, divisional commissioner Aminur Rahman told AFP late Saturday.
The rain and wind were felt in Myanmar's commercial hub Yangon, around 500 kilometres away, residents said Sunday.