The Marlin Luanda went up in flames on Friday after Houthi threats to shipping in the region persisted, despite a joint US-UK strikes against rebel sites in Yemen earlier this week.
Speaking on Saturday, Mr Shapps said: "This intolerable and illegal attack on maritime shipping is the latest on innocent people and global trade.
“It is our duty to protect freedom of navigation in the Red Sea and we remain as committed to that cause as ever.”
The Marlin Luanda sails under the flag of the Marshall Islands but is managed by Oceonix Services Ltd, a company registered in the UK.
It is operated on behalf of Trafigura, a multinational trading giant domiciled in Singapore.
Trafigura said a fire in the ship’s cargo tank had been extinguished with the help of Indian, US and French Navy vessels and all crew were safe.
“The vessel is now sailing towards a safe harbour. The crew continues to monitor the vessel and cargo closely,” a spokesperson said.
“We would like to recognise the exceptional dedication and bravery of the ship’s master and crew who managed to control the fire in highly difficult circumstances, as well as the essential assistance provided by Indian, United States and French Navy vessels to achieve this outcome.”
The UK and its allies “reserve the right to respond appropriately” following the latest attack claimed by the Iran-backed group, the Government said.
The fire came after another incident in the region on Friday, in which two missiles were reported to have exploded in the water and “vessel and crew are safe and no damage reported”.
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 was carried out at the start of the week, while both nations have issued a wave of sanctions targeted at individuals.
But the steps appear to have done little to deter the Houthis' action.
On Saturday, UK Maritime Trade Operations also reported a vessel 780 nautical miles east of Hafun, Somalia, was also approached by a small craft with four people.
Automatic rifles and a rocket propelled grenade were spotted, but the boat retreated after the onboard security team fired warning shots as it approached to within 300 metres, it said.
The British Government said in response to the Marlin Luanda attack: “We are aware of reports that the M/V Marlin Luanda, a Marshall Islands-flagged tanker, has sustained damage from attack in the Gulf of Aden.
“Current reports suggest no casualties and nearby coalition vessels are on the scene.
“We have been clear that any attacks on commercial shipping are completely unacceptable and that the UK and our allies reserve the right to respond appropriately.”
Foreign Secretary Lord Cameron this week embarked on a trip the Middle East in a diplomatic bid to reduce tensions as the Israeli bombardment of Gaza continues.