The Houthis' biggest territorial gains in years, along the Bab el-Mandeb Strait, could boost Iran's strategy of driving up world oil and gas prices to pressure the United States.
The capture of Mayun, a tiny, barren volcanic island inside the strait also known as Perim, was confirmed by a senior military official with Yemen's internationally recognised government and by a Houthi official.
Both spoke on condition of anonymity because they were not authorised to talk to journalists.
Saudi Arabia, the world's largest oil exporter, has increasingly relied on the Red Sea to get its crude to market as an alternative to the Strait of Hormuz, where Iran has been striking ships.
Houthi moves to close the 28km-wide Bab el-Mandeb channel have made that route more complicated.
In a statement on Friday, the Houthi armed forces boasted of gains along the coast.
They vowed "escalation for escalation" in their confrontation with Saudi Arabia, while declaring that "maritime navigation is safe for all companies except for Saudi vessels".
Financial markets are nervous, and experts have described the Houthis as highly unpredictable. Crude prices this week soared once again above $US100 a barrel, giving Tehran more leverage in any talks.
The Houthis have been attacking Saudi shipping on the Red Sea since declaring a blockade in July, as well as oil infrastructure inside Saudi Arabia.
The rebels said they acted in response to the kingdom's years-long blockade of Houthi-held parts of Yemen.
Shipping through the Bab el-Mandeb Strait had fallen by about 60 per cent since the Houthis began attacking ships there in late 2023 and expressing solidarity with Palestinians in Gaza.
Shipping increased this year as Saudi Arabia sought alternatives to the Strait of Hormuz, but renewed Houthi threats have "curtailed" that activity, according to Lloyd's List Intelligence.
That has forced Saudi Arabia to find yet another alternative, sending its oil north out of the Red Sea to the Mediterranean, either via the Suez Canal or a pipeline through Egypt, a far longer route for its clients in Asia.
The Houthis have threatened that route as well, striking a Saudi vessel in the north of the Red Sea in late August.
Earlier on Friday, Iran's government called for an end to Saudi Arabia's blockade of Houthi-held areas in a show of support for its ally.
The Iranian Foreign Ministry also called for a return to negotiations between Saudi Arabia and the Houthis.
In a sign of how important the Houthis have become for Tehran, the spokesperson for Iran's powerful Revolutionary Guard on Wednesday called for any negotiated settlement with the US to include Yemen, the first explicit reference to that front.
The call mirrored Iran's past stance that a truce in Lebanon between its ally Hezbollah and Israel must be a part of any deal with the US.
As the Houthis swept along the Red Sea coast toward the Bab el-Mandeb channel, Yemen's Saudi-backed government called for international support.
The escalating fighting threatens to end a fragile truce that had largely halted Yemen's civil war since 2022.
At stake are the 40 million people in the Arab world's poorest country who fear a return to the conflict that killed 150,000 and brought many others to the brink of famine.
