An intense cyclone smashed into the low-lying coast of Bangladesh on Sunday, with nearly a million people fleeing inland for concrete storm shelters away from howling gales and crashing waves.

"The severe Cyclone Remal has started crossing the Bangladesh coast," Bangladesh Meteorological Department Director Azizur Rahman said, adding the raging storm could continue hammering the coast until at least the early hours of Monday morning.

"We have so far recorded maximum wind speeds of 90 kilometres per hour, but the wind speed may pick up more pace."

Forecasters predicted gusts of up to 130 kilometres per hour, with heavy rain and winds also lashing neighbouring India.

Authorities have raised the danger signal to its highest level.

Cyclones have killed hundreds of thousands of people in Bangladesh in recent decades, but the number of superstorms hitting its densely populated coast has increased sharply, from one a year to as many as three, due to the impact of climate change.

"The cyclone could unleash a storm surge of up to four metres above normal astronomical tide, which can be dangerous," Bangladeshi senior weather official Muhammad Abul Kalam Mallik said.

Most of Bangladesh's coastal areas are a metre or two above sea level and high storm surges can devastate villages.

"We are terrified," said 35-year-old fisherman Yusuf Fakir at Kuakata, a town on the very southern tip of Bangladesh in the predicted route of the storm, speaking just before its arrival.

At least 800,000 Bangladeshis fled their coastal villages, while more than 50,000 people in India also moved inland from the vast Sundarbans mangrove forest, where the Ganges, Brahmaputra and Meghna rivers meet the sea, government ministers and disaster officials said.

"We want to ensure that a single life is not lost," said Bankim Chandra Hazra, a senior minister in India's West Bengal state.

India's Kolkata airport closed on Sunday, while the Indian navy readied two ships with aid and medical supplies for "immediate deployment". (AFP)