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.
Ambrey said the master was heard over VHF, calling a coalition warship.
It said 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.
Ambrey said it understood that three missiles had been fired from the direction of Yemen's Taiz Governorate.