The sudden burst of attacks by the Houthis comes after an unexplained pause of a week and a half by the rebels.
It is though they might be regrouping before the arrival of a new US aircraft carrier to the region after the USS Dwight D Eisenhower began heading home.
Wednesday's attack targeted a ship south of Mocha, the British military's United Kingdom Maritime Trade Operations centre said.
The captain reported explosions off the ship's side.
The "vessel and all crew are safe", the UKMTO said and the vessel was going to its next port of call.
The Houthis have been attacking ships in the Red Sea corridor since November.
The rebels did not immediately claim Wednesday's attack, although they often do not do so for hours or even days.
On Tuesday, the Houthis said they launched missiles at a US-flagged container ship in the Gulf of Aden.
The Joint Maritime Information Centre (JMIC), which is overseen by the US Navy, identified the ship as the Maersk Sentosa and warned it was the longest-distance attack seen from Yemen by the Houthis since November
Late on Tuesday night, the Houthis issued a broad claim of responsibility for three attacks, which included the Maersk Sentosa.
Maersk, a Danish firm that is the world's biggest shipping company, did not immediately comment.
The rebels have targeted more than 70 vessels by firing missiles and drones in their campaign that has killed four sailors.
They have seized one vessel and sunk two since November.
In June, the number of Houthi attacks on merchant vessels increased to levels not seen since December, according to the JMIC.
US-led air strikes have been targeting the Houthis since January, with a series of strikes on May 30 killing at least 16 people and injuring 42 others, the rebels say.
The Houthis maintain their attacks target ships linked to Israel, the United States or Britain as part of rebel support for the militant group Hamas in its war against Israel in the Gaza Strip.
However, many of the ships attacked have little or no connection to the Israel-Hamas war, including some bound for Iran.
The sudden increase in assaults comes after a relatively quiet week and a half.
The rebels gave no explanation for the suspension or the resumption of attacks.
However, the aircraft carrier USS Theodore Roosevelt is due to enter the Middle East region to replace the USS Dwight D Eisenhower, which had spent months in the Red Sea to counter the Houthis.
