Many residents took shelter in schools and caves as Chapala brought hurricane-force winds, heavy rain and powerful waves to the island.
Photos and videos posted online showed water flowing through the streets of the provincial capital, Hadibu.
It is believed to be the most powerful storm that Yemen has seen in decades.
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 reported that Chapala was generating gusts of up to 150mph, equivalent to a category 4 hurricane.
Gusts of up to 100 mph are forecast for when the storm makes landfall just west of the city of Mukalla, on the south coast of the Yemeni mainland, on November 3.
The cyclone could 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.
The US House Ethics Committee has voted to release its report on former Republican Representative…
ABC News has agreed to pay $15 million to President-elect Donald Trump to settle a…
South Korea’s parliament has voted to impeach President Yoon Suk Yeol over his failed attempt…
Israeli war planes have carried out more than 100 air strikes in Syria on December…
President-elect Donald Trump has threatened to impose 100% tariffs on the BRICS countries if they…
Syrian troops have withdrawn from the city of Aleppo following an offensive by rebels opposed…