Twelve suspects, including the wounded, were taken into custody after the early morning gun battle , said Lt Cmdr. Charlie Brown, spokesman for the US navy's 5th Fleet, on Sunday.
The nationalities and identifications of the suspected pirates were unknown.
The shootout early on Saturday ensued after the navy ships, patrolling the area as part of a Dutch-led coalition task force, spotted the suspect 30-foot-long fishing boat towing smaller skiffs and prepared to board and inspect the vessels, Brown told The Associated Press.
A statement from the Bahrain-based 5th Fleet said the suspected pirates were holding what appeared to be rocket-propelled grenade launchers.
When the suspects began shooting, naval gunners on the US ships returned fire with mounted machine guns, killing one man and igniting a fire on the vessel.
Three suspects were seriously wounded and being treated on one of the navy ships, Brown said. A Dutch navy medical team was en route aboard the HNLMS Amsterdam. No US sailors were injured in the gun battle.
Pirate attacks surged to 35 last
year from two in 2004 (File pic)
The navy boarding teams confiscated an RPG launcher and automatic weapons, the statement said.
The navy said the incident involving the Norfolk, Virgina-based USS Cape St. George and USS Gonzalez occurred at about 5:40 am local time, approximately 25 nautical miles off the Somali coast in international waters.
The International Maritime Organisation has warned ships to stay away from the Somali coast because of pirate attacks, which surged to 35 last year from two in 2004.
On March 15, the UN Security Council encouraged naval forces operating off Somalia to take action against suspected piracy. Pirate attacks against aid ships have hindered UN efforts to provide relief to the victims of a severe drought in the area.
The pirate raids are part of the anarchy wracking Somalia, which has had no effective government since 1991, when warlords ousted a dictatorship and then turned on each other.