Two people are still missing and dozens have been hurt by Cyclone Megh, the minister, Fahd Kafayen, said early on Tuesday.
"There is also widespread destruction of residents' homes and fishermen's equipment and on farms and livestock," Kafayen said in a post on his Facebook page, Reuters reported.
Megh, which has caused about 5,000 people to flee their homes, is expected to hit Yemen's coast east of Aden as a severe cyclonic storm Tuesday, with sustained winds of 90 km-120 km (56-75 mph), the World Meteorological Organization said.
The UN humanitarian coordination office has said more than 230,000 people on the Yemeni mainland will be exposed to high winds and heavy rainfall, with the governorates of Abyan and Al Bayda most at risk.
Cyclone Megh follows Cyclone Chapala, which killed 11 Yemenis on Socotra and the mainland, dumping nearly a decade of average annual rainfall on the impoverished and war-wrecked country in just two days. That cyclone displaced some 18,000 people, about a third of Socotra's population.
Socotra, 380 km (238 miles) off Yemen in the Arabian Sea, is home to 50,000 residents who have long been isolated from the mainland and speak their own language, Socotri.
More than a third of Socotra's population, 18,000 people, were displaced by Chapala, according to the United Nations.