London's warning comes amid escalating tensions in the vital shipping lane, with US Navy helicopters firing Sunday on Houthi rebels who attempted to board a cargo ship.
The rebels, who seized Yemen's capital Sanaa in 2014 and control much of country including its Red Sea coastline, have reported 10 fighters dead or missing.
The Houthis — who say they are acting in solidarity with Palestinians in the Israel-Hamas war in Gaza— have repeatedly fired drones and missiles at passing ships in the seaway through which 12 percent of global trade passes.
Hours after the latest incident, Shapps said Britain could step up its own military interventions. A British destroyer shot down a suspected Houthi attack drone in the Red Sea in mid-December.
"We are willing to take direct action, and we won't hesitate to take further action to deter threats to freedom of navigation in the Red Sea," he wrote in the Daily Telegraph newspaper.
The Houthis "should be under no misunderstanding: we are committed to holding malign actors accountable for unlawful seizures and attacks."
Shapps described the situation in the region as "a test for the international community" which had implications for other potentially contested waterways around the world.
"If we do not protect the Red Sea, it risks emboldening those looking to threaten elsewhere including in the South China Sea and Crimea," he added.
"We need to stand firm with our allies, stand firm for our beliefs and stand firm for innocent people caught up in these events."
The Telegraph said London is drawing up plans with Washington for potential military strikes against the Houthis, and reported that a joint statement giving the rebels a final warning to stop their attacks was imminent.
British Foreign Secretary David Cameron said Sunday he had spoken to his Iranian counterpart Foreign Minister Hossein Amir-Abdollahian about the Red Sea tensions.
"I made clear that Iran shares responsibility for preventing these attacks," he said on social media, noting Tehran's "long-standing support" for the Houthis.
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