The cause of the Black Hawk helicopter's crash is unknown.
Five others aboard the aircraft were rescued, officials said in a statement issued by U.S. Central Command.
A search is ongoing for the missing service member and the USA military said it will investigate the incident.
Officials have not provided information on the identities of those on board or the unit to which the aircraft belongs, saying only that the incident occurred around 7 p.m. local time about 20 miles off Yemen's southern coast.
A small number of ground raids using U.S. Special Operations forces have also taken place, including one in January which resulted in the death of a U.S. Navy Seal.
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The crash isn't the first one for a military helicopter in 2017.
Known as al-Qaida in the Arabian Peninsula, the group rose to prominence in 2009 and has taken advantage of a civil war in Yemen to increase its influence in the region.
"U.S forces in the region are conducting an ongoing search for one US service member who was aboard the aircraft", the military said in a statement.
The group is al-Qaida's second largest affiliate and perhaps its most unsafe, USA defense officials speaking on condition of anonymity told reporters in a briefing earlier this year.
The crash took place Friday evening.