Defence Secretary Grant Shapps said the incident overnight saw the warship use its Sea Ceptor missiles to repel the attack.
The US Central Command said a total of 15 drones were shot down by coalition vessels and aircraft during attacks in Red Sea and Gulf of Aden in the early hours of Saturday morning.
Defence Secretary Grant Shapps said: “The UK and our allies will continue to take the action necessary to save lives and protect freedom of navigation.”
The Ministry of Defence said the Type 23 frigate and international allies “fully repelled” a Houthi drone attack with no injuries or damage sustained.
The MoD said Richmond’s crew acted in an “exemplary manner” and the UK was “unwavering in our position that we will take the action necessary to protect innocent lives and the global economy”.
The Houthis, based in Yemen, have claimed their attacks on shipping in the Red Sea are in response to events in Gaza, although the merchant vessels targeted have often had little or no link to Israel.
The attacks on vessels using the Red Sea have resulted in ships diverting around southern Africa rather than using the Suez Canal between Europe and Asia, adding to costs and creating a potential global economic risk.
The US Central Command said American and coalition forces acted after determining the “large scale uncrewed aerial vehicle” attack “presented an imminent threat to merchant vessels”.
