The Iran-backed Houthis are also reported to have seized Perim - a strategic island on the major shipping route.
The capture by the rebels of a stretch of Yemen's strategic coastline is the group's most impressive military coup for several years.
Yemen's Houthis have seized territory near the Bab al-Mandab Strait - a key trade gateway for oil and global shipping.
Iran's proxy says it hit a ship with Saudi military equipment in the Red Sea, as tensions over the US-Iran war remain high.
The Houthis say they launched missiles and drones at "Saudi military build-ups" in the central provinces of Marib and Hadramawt.
US military says it disabled a tanker that was attempting to evade the American blockade on Iranian ports.
It comes as Iran condemned the US plan to use frozen Iranian assets to pay for war damages.
The Iran-backed group in Yemen has threatened to target Saudi vessels in a vital shipping route.
The Iran-backed group, which previously announced a "maritime embargo" against Saudi Arabia, also claims to have hit another vessel.
