The storm presaged the approach of cyclone Chopala which is expected to hit the Yemeni mainland and Oman on Monday.
"More than 80 houses were damaged on the coast of Socotra and hundreds of people were rescued and hospitalised," Salem Zaher, the mayor of Hadibou, the island's main town, told AFP.
"More than a thousand families were evacuated and resettled in schools and camps" inland amid "intense rainfall and strong winds", he added.
The UN's weather agency said on Friday that the "super cyclonic storm" named Chapala was expected to make landfall at around midnight on Monday in Yemen and Oman.
On Saturday, Yemen's meteorological agency called on residents of the southeastern provinces of Hadramawt and Mohrah -- and people on Socotra -- to stay at least one kilometre (nearly a mile) from the coast.
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Socotra island is less than 250 kilometres from the Horn of Africa and 350 kilometres off the Yemeni mainland.
It has 50,000 inhabitants, mostly fishermen.
The UN's World Meteorological Organization has described Chapala as "an extremely severe cyclonic storm".
It said Chapala's wind speed was the equivalent of a category four hurricane.
Omani authorities ordered schools closed on Sunday and Monday in the southwestern province of Dhofar, ONA state news agency said.
It said satellite images have shown that Chapala was approaching the shores with wind speeds between 220 and 250 kilometres (136 and 155 miles) per hour.
Oman's civil aviation authority warned that waves higher than seven metres (23 feet) were expected to hit the beaches of Dhofar.