British maritime security firm Ambrey said on Tuesday that a Malta-flagged container ship reported seeing three explosions towards its port quarter, 15 miles (24 km) southwest of Yemen's Mocha.
The vessel master was heard over VHF, calling a coalition warship, the firm added.
Ambrey said it understood that three missiles had been fired from the direction of Yemen's Taiz Governorate.
A nearby vessel reported seeing a small boat, about 50 metres (160 feet) in length, and with two lights, within 1 mile (1.6 km) of the incident location soon afterwards, the firm added.
Yemen's Iranian-backed Houthi militants, who control much of Yemen including the capital Sanaa, have stepped up attacks on commercial vessels in the Red Sea in protest against Israel's war in Gaza.
"It was assessed this particular vessel was not Israel-affiliated, but other vessels in the operator's fleet had regularly called Israel, and this affiliation might have been sufficient for her to be targeted," Ambrey said.
Several shipping lines have suspended operations through the Red Sea in response to the attacks, instead taking the longer journey around Africa.
The Houthis have vowed to continue their attacks until Israel halts the conflict in Gaza, and warned that it would attack U.S. warships if the militia group itself was targeted.
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