HMS Diamond was defending a merchant vessel in the Gulf of Aden on Wednesday when her Sea Viper missile system was used to destroy the projectile, the Ministry of Defence (MoD) said.
The warship is currently deployed in the region to deter Houthi attacks.
Defence Secretary Grant Shapps thanked the crew for helping to “save innocent lives” and protect shipping.
“The UK continues to be at the forefront of the international response to the Iranian-backed Houthis’ dangerous attacks on commercial vessels, which have claimed the lives of international mariners,” he added.
He told The Times that it was the first time a Royal Navy warship had intercepted a missile in combat since the Gulf War in 1991.
The Houthis – who control large swathes of Yemen, including the capital Sanaa – have been targeting vessels they say are linked to Israel and the West in response to the continuing Israel-Gaza war.
Global supply chains are now facing severe disruption and rising costs as a result of some of the biggest shipping companies diverting journeys away from the Red Sea – one of the world’s busiest shipping lanes.
On Wednesday, the Houthis claimed to have attacked the US ship Maersk Yorktown and an American destroyer in the Gulf of Aden.
The MoD said HMS Diamond’s deployment in the Red Sea and Gulf of Aden forms part of the UK’s wider response to Houthi attacks.
This includes intercepting the smuggling of weapons to Yemen, imposing sanctions on members of the Houthis, and conducting proportionate and targeted strikes against its military targets.
HMS Diamond previously operated in the region in December and January, and came under fire in three separate attacks by Houthi forces, successfully destroying nine drones with the Sea Viper missile system and guns.
Earlier this year, the warship took over from HMS Richmond, which had repelled a Houthi attack in the Red Sea by shooting down two drones using Sea Ceptor missiles.
HMS Diamond is equipped with Sea Viper missiles, as well as Phalanx machine guns and 30mm cannons on each side of the ship. The Phalanx can fire more than 3,000 rounds a minute. The crew have also used the 30mm cannon to successfully shoot down a Houthi drone.
The US and UK started carrying out air strikes on Houthi targets in Yemen on 11 January. There have been several more strikes since then.
In response, the Houthis have more recently targeted ships tied to owners or operators in the UK or US.
