The forces carried out "a military operation targeting a British ship... while it was sailing through the Gulf of Aden", military spokesman Yahya Saree said on social media.
Two Western maritime security agencies earlier reported an explosion near a vessel off the coast of Yemen.
The United Kingdom Maritime Trade Operations said the ship reported "an explosion in close proximity to the vessel" east of Yemen's Aden, adding the vessel was sailing to its next port of call.
Security firm Ambrey said a "bulk carrier was targeted by an explosive projectile whilst transiting" east of Aden.
The projectile, Ambrey said, exploded off the vessel and caused "minor damage due to shrapnel impacting a diesel generator pipe which led to a diesel leak".
Yemen’s armed forces have been targeting Israeli ships and those bound for Israeli ports since November in solidarity with the Palestinians in Gaza which has been subject to five months of ferocious airstrikes and a ground invasion.
The Yemeni operations have prompted some shipping companies to detour around southern Africa to avoid the Red Sea, which normally carries about 12 percent of global maritime trade.
The Yemeni army says only Israeli, US and British ships are targeted, stating that other countries can rest assured of the safety of their cargoes.
Last November, UK-owned ship The Galaxy Leader sailing through the Red Sea was hit by rocket fire, according to Ambrey.
Yemen has declared an open war against US and British interests since the two countries launched a military campaign against the Arab country in support of Israel.
On Thursday, the US military said it conducted strikes against what it claimed as mobile anti-ship cruise missiles, mobile unmanned aerial vehicles, and an explosive unmanned surface vessel in Yemen.
Yemen’s Saba news agency reported several strikes on the Red Sea coastal province of Hudaydah.
CENTCOM said an anti-ship ballistic missile was launched from Yemen into the Gulf of Aden.