The missiles, which hit commercial vessels Unity Explorer and Number 9, were reportedly fired from Houthi-controlled areas of Yemen.
Both vessels were said to have suffered minor damage but there were no reported casualties. The Houthis in Yemen are backed by Iran.
Britain's Defence Secretary Grant Shapps said: "I strongly condemn the outrageous and unlawful attacks on ships by Iran backed Houthi militants."The UK is committed to protecting maritime security & deterring escalation, with HMS Diamond deploying to the region as part of the UK’s efforts to ensure regional stability."
I strongly condemn the outrageous and unlawful attacks on ships by Iran backed Houthi militants.
The UK is committed to protecting maritime security & deterring escalation, with HMS Diamond deploying to the region as part of the UK’s efforts to ensure regional stability.
— Rt Hon Grant Shapps MP (@grantshapps) December 4, 2023
US Central Command said: “We have every reason to believe that these attacks, while launched by the Houthis in Yemen, are fully enabled by Iran.
“The United States will consider all appropriate responses in full coordination with its international allies and partners.”
It added that the Unity Explorer is a Bahamas flagged, UK owned and operated, bulk cargo ship crewed by sailors from two nations and the M/V Number 9 a Panamanian flagged, Bermuda and UK owned and operated, bulk carrier.
A spokesman for the Number 9 ship managers, Bernhard Schulte Shipmanagement, said: “All crew onboard are accounted for and safe.
“Our priorities are to ensure the continued safety of the crew and vessel.”
The owner of the ship is understood to be Castle Harbour Capital, a UK company.
The attacks will raise fears that the Israel-Hamas conflict could escalate into a wider Middle East war.
In London, the Prime Minister's official spokesman said: "We condemn the attack on commercial shipping in the Red Sea by Houthi militants.
"As we've previously said, Iran has long provided political and military support to Houthi militants and it bears responsibility for the actions of its proxies and partners.
"These waters are vital routes for global trade and incidents like these show the importance of the Royal Navy's presence in the region."
Type 45 destroyer HMS Diamond was already heading to the region to bolster the navy's presence there.
In a statement on Twitter, also known as X, US Central Command said one of its warships, the USS Carney, was also attacked.
The authority said: “Today, there were four attacks against three separate commercial vessels operating in international waters in the southern Red Sea.
"These three vessels are connected to 14 separate nations. The Arleigh-Burke Class destroyer USS Carney responded to the distress calls from the ships and provided assistance.
It added: "These attacks represent a direct threat to international commerce and maritime security. They have jeopardised the lives of international crews representing multiple countries around the world."
Yemen's Houthi movement said its navy had attacked two Israeli ships, Unity Explorer and Number 9, with an armed drone and a naval missile.
A spokesperson for the group's military said the two ships were targeted after they rejected warnings, without elaborating.
In a broadcast statement the spokesperson said the attacks were in response to the demands of the Yemeni people and calls from Islamic nations to stand with the Palestinian people.
An Israeli military spokesman Rear Admiral Daniel Hagari said the two ships had no connection to Israel.
"One ship was significantly damaged and it is in distress and apparently is in danger of sinking and another ship was lightly damaged," Hagari told reporters in Tel Aviv.
The Bahamas-flagged bulk carrier Unity Explorer is owned by Unity Explorer Ltd and managed by London-based Dao Shipping Ltd, LSEG data showed. The ship was scheduled to arrive in Singapore on December 15.
Number 9, which was headed to Suez port, is a Panama-flagged container ship owned by Number 9 Shipping Ltd and managed by Newcastle-upon-Tyne, UK-based Bernhard Schulte Shipmanagement (BSM), the data showed.
BSM said in a statement to Reuters Number 9 is currently sailing and there were no reports of injuries or pollution after the incident. The vessel was hit by a projectile while transiting the Bab al-Mandab Strait, the company said.
Unity Explorer's owners and managers could not be reached immediately by Reuters for comment.
The Pentagon said it was aware of reports regarding attacks on an American warship and commercial vessels in the Red Sea on Sunday, as Yemen's Houthi group claimed drone and missile attacks on two Israeli vessels in the area.
"We're aware of reports regarding attacks on the USS Carney and commercial vessels in the Red Sea and will provide information as it becomes available," the Pentagon said.
Today, there were four attacks against three separate commercial vessels operating in international waters in the southern Red Sea. These three vessels are connected to 14 separate nations. The Arleigh-Burke Class destroyer USS CARNEY responded to the distress calls from the…
— U.S. Central Command (@CENTCOM) December 3, 2023
The reported incident follows a series of attacks in Middle Eastern waters since war broke out between Israel and the Palestinian militant group Hamas on October 7.
An Israeli-linked cargo ship was seized last month by the Houthis, allies of Iran. The group, which controls most of Yemen's Red Sea coast, had previously fired ballistic missiles and armed drones at Israel and vowed to target more Israeli vessels.
ABC News, citing a US official, said the USS Carney had been involved in multiple engagements involving Houthi attacks on commercial vessels.
"In at least two circumstances, the Carney successfully shot down (drones) headed in its direction," the official told ABC.
British maritime security company Ambrey and sources said earlier that a bulk carrier and a container ship had been hit by at least two drones while sailing in the Red Sea.
Ambrey said the container ship had reportedly suffered damage from a drone attack about 63 miles northwest of the northern Yemeni port of Hodeidah.
Britain's Maritime Trade Operations agency (UKMTO) said it had received reports of a drone attack in the Red Sea's Bab al-Mandab strait.
Last week a US Navy warship responded to a distress call from an Israeli-managed commercial tanker in the Gulf of Aden after it had been seized by armed individuals.