Cyclone Chapala has hit the Yemeni mainland bringing hurricane-force winds, heavy rain and powerful waves.
Photos and videos posted online showed water pouring through the streets of the southern coastal city of Mukalla.
Mukalla is controlled by al-Qaeda and correspondents say it is ill-equipped to deal with a disaster.
Earlier, Cyclone Chapala hit the remote Yemeni island of Socotra, killing at least one person.
Many residents there took shelter in schools and caves.
The UN’s World Meteorological Organization described the cyclone as “extremely severe”, and said that sea conditions around the centre of the storm were “phenomenal”.
On November 2, the US Navy’s Joint Typhoon Warning Centre (JTWC) reported that Chapala was generating gusts of up to 150mph, equivalent to a category 4 hurricane.
The JTWC said Chapala would begin to weaken as dry air emanating from the Arabian Peninsula eroded the storm system, and that it would rapidly decay after landfall mainly due to the interaction with the rugged and dry Yemeni terrain.
Cyclone Chapala could nevertheless deluge parts of the country with up to 20in of rain in two days – 10 times the annual average.
Socotra is situated 230 miles south of the coast of Yemen in the Arabian Sea, to the east of Somalia.
It is home to about 50,000 people, who speak their own language, and hundreds of exotic plant species found nowhere else on earth, including dragon’s blood trees.
The mayor of Hadibu, Salem Zaher, told the AFP news agency that Chapala had damaged more than 80 houses and left hundreds of people needing hospital treatment.
More than 1,000 families had been evacuated and resettled in schools and camps inland before the storm hit, he added.
Residents of Mukalla, which has been controlled by a tribal council and jihadist militants from al-Qaeda in the Arabian Peninsula (AQAP) since April, meanwhile expressed concern about local preparations for when Chapala made landfall.