Crew on the ship successfully repelled a drone strike from the rebel group in the Red Sea, the Ministry of Defence (MoD) has said.
No injuries or damage were sustained, the MoD added.
In a post on X, Mr Shapps wrote: “The UK remains undaunted after yesterday’s illegal attack on @HMSDiamond by the Iranian backed Houthis. Our commitment to protect innocent lives and the freedom of navigation is absolutely unwavering.”
The MoD earlier branded ongoing action by the Houthis “intolerable and illegal”, and said Britain and its allies “reserve the right to respond appropriately”.
The fire on the Marlin Luanda was extinguished with no crew injured after French, Indian and US naval ships provided assistance to the vessel.
The ship sails under the flag of the Marshall Islands but is managed by Oceonix Services Ltd, a company registered in the UK.
The Yemeni forces claimed on Friday they had targeted a “British oil” vessel following “American-British aggression against our country”.
The Houthis have repeatedly launched attacks on vessels around the Red Sea over Israel’s war on Hamas in Gaza, although they have frequently targeted ships with tenuous or no clear links to Israel, endangering shipping on a key global trade route.
A second series of UK and US air strikes, carried out at the start of the week, appears to have done little to thwart their action.
British warships cannot attack Houthi targets on land because they lack the firepower, according to a report.
The US has carried out the majority of strikes on Houthi targets with support from RAF planes based 1,500 miles away.
HMS Diamond, the destroyer stationed in the Red Sea, lacks “the capability to fire to land targets”, a British defence source told the Sunday Telegraph.
A Ministry of Defence spokesperson said: “As with all coalition operations, commanders select the best equipment for the job. HMS Diamond is an air defence destroyer, which has been directly involved in successfully destroying Houthi drones targeting shipping in the Red Sea.
“Equally, the Royal Air Force has the capability to strike land targets with high precision, which is why Typhoon aircraft strikes have reduced the Houthis’ ability to conduct these attacks.”
The Foreign Secretary this week embarked on a trip to the Middle East in a bid to reduce tensions amid fears the war in Gaza could spiral into a wider regional conflict.
Writing in The Mail on Sunday on his return, Lord Cameron argued a new international group comprising the US, UK, key EU states, Gulf and Arab countries and Turkey should be established to broker an end to the fighting.
“Let’s use a pause in the fighting to build unstoppable momentum towards a lasting solution,” he wrote.