The archipelago was struck by Cyclone Mekunu on Wednesday night, leaving at least 17 people missing and forcing its native population to flee floodwaters.
Socotra is part of Yemen, which is embroiled in a lengthy civil war - something from which the four islands have largely been spared.
But after two boats capsized during the cyclone, and at least three cars were washed away by powerful floods, the government has declared Socotra a disaster zone.
Media captionResidents sought shelter from the knee-deep torrential floodwaters
Coastal areas "were submerged by floods causing heavy damage to homes," a spokesman told AFP.
Hundreds have been evacuated from villages, but rescue workers are reportedly unable to reach many people in isolated parts of the main island.
Officials have appealed to international aid agencies for help.
Home of the blood dragon
Socotra is famed for its natural beauty.
Its startling biodiversity has earned it the nickname "Galapagos of the Indian Ocean" - a nod to Ecuador's famous Pacific island chain whose ecosystem is so unique it inspired Charles Darwin's theory of evolution.
The link to the famed Galapagos is not purely marketing either. Since it was first surveyed by United Nations' biologists in 1997, Socotra has been considered one of the most biologically diverse and distinct places on Earth.
It's estimated that 37% of its plants and 90% of its reptiles (along with almost all of its snails) are found nowhere else on earth, and the entire island chain is a registered Unesco World Heritage site.
One of the most iconic of its native species is the blood dragon tree - a striking, umbrella-shaped tree with a thick trunk