Ambrey said a radio communication indicated the ship was hit by a missile and that there was a fire onboard about 10 nautical miles southwest of Mokha.
It had received assistance and one of its steering units was functional, Ambrey added, citing information it had received but without giving more details.
Other vessels in the vicinity were advised to exercise caution, Ambrey added in an advisory note.
Separately, the United Kingdom Maritime Trade Operations (UKMTO) agency said earlier on Saturday that a vessel in the Red Sea was struck by an unknown object and sustained slight damage.
"The vessel and crew are safe and continuing to its next port of call," UKMTO said in an advisory note on the incident 98 nautical miles south of Yemen's Hodeidah port.
