HMS Diamond, currently deployed in the Red Sea and Gulf of Aden, downed the missile on Wednesday using its Sea Viper anti-air missile system.
The Ministry of Defence said that in addition to stationing warships in the area, the UK has also intercepted weapons being smuggled into Yemen, carried out targeted strikes against Houthi military targets and imposed sanctions on the group’s members.
Defence Secretary Grant Shapps said: “I want to thank the brave crew of HMS Diamond for her vital role in saving innocent lives and protecting international shipping from illegal Houthi attacks.
“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.”
In March, HMS Diamond took over shipping protection duties in the area from HMS Richmond, which repelled two Houthi drone attacks in the Red Sea using its Sea Ceptor missiles, the MoD said.
The Type 45 destroyer, which had previously operated in the region in December and January, is equipped with Sea Viper missiles as well as Phalanx machine guns and 30mm cannons on each side of the ship.
The Yemen-based Houthi group has claimed its attacks on shipping in the Red Sea are in response to events in Gaza, although targeted merchant vessels often had little or no link to Israel.
The attacks on vessels using the Red Sea have resulted in some ships re-routing around southern Africa rather than using the Suez Canal between Europe and Asia, a much lengthier journey which has driven up shipping costs and caused delays.
The MoD added the UK “remains committed” to protecting the Red Sea and Gulf of Aden from “indiscriminate” and “illegal” Houthi attacks, which it said continue to “harm the global economy and undermine the stability and security of Yemen”.