The attack on the ship came as the US military acknowledged conducting new air strikes targeting the rebels, including one that targeted the first Houthi underwater drone seen since the rebels' began launching their attacks on shipping in November.
The ship targeted in the Houthi attack on Sunday reported sustaining damage after "an explosion in close proximity to the vessel", the British military's Maritime Trade Operations Centre reported.
"Military authorities report crew have abandoned the vessel," it said.
"Vessel at anchor and all crew are safe."
Houthi Brigadier General Yahya Saree issued a statement claiming the attack, saying the vessel was "now at risk of potentially sinking".
"The ship suffered catastrophic damages and came to a complete halt," Saree said.
"During the operation, we made sure that the ship's crew exited safely."
The private security firm Ambrey reported the British-registered, Lebanese-operated cargo ship had been on its way to Bulgaria after leaving Khorfakkan in the United Arab Emirates.
Ship-tracking data from MarineTraffic.com analysed by The Associated Press identified the vessel targeted as the Rubymar.
Its Beirut-based manager could not be immediately reached for comment.
The Houthis later also identified the ship as the Rubymar.
Ambrey described the ship as being partially laden with cargo, but it wasn't immediately clear what it had been carrying.
The ship had turned off its identification tracker while in the Persian Gulf early this month.
Since November, the rebels have repeatedly targeted ships in the Red Sea and surrounding waters over Israel's war targeting Hamas in the Gaza Strip.
They have frequently targeted vessels with tenuous or no clear links to Israel, imperilling shipping in a key route for trade among Asia, the Middle East and Europe.
Those vessels have included at least one with cargo for Iran, its main benefactor.
Meanwhile, the US military's Central Command reported it carried out five air strikes targeting Houthi military equipment.
Those strikes targeted mobile anti-ship cruise missiles, an explosive-carrying drone boat and an "unmanned underwater vessel", Central Command said.
"This is the first observed Houthi employment of a UUV since attacks began in October 23," it said.
