Twelve suspects were taken into custody after the early-morning shootout, said Lt. Cmdr. Charlie Brown, spokesman for the U.S. Navy's 5th Fleet.
No sailors were wounded in the battle, which occurred at about 5:40 a.m. local time, approximately 25 nautical miles off the Somali coast in international waters.
The battle started after the USS Cape St. George and USS Gonzalez, which were patrolling as part of a Dutch-led task force, spotted a 30-foot fishing boat towing smaller skiffs and prepared to board and inspect the vessels.
The suspected pirates were holding what appeared to be rocket-propelled grenade launchers, the navy said. When the suspects began shooting, naval gunners returned fire with mounted machine guns.
Three suspects were seriously wounded and being treated on one of the Navy ships, Brown told The Associated Press. A Dutch Navy medical team was en route.
The suspects' nationalities were unknown.
The Navy boarding teams confiscated an RPG launcher and automatic weapons, the statement said.
The Cape St. George, a guided-missile cruiser, and Gonzalez, a guided-missile destroyer, were conducting maritime security operations in the area. They are based in Norfolk, Va.
The International Maritime Organization 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 U.N. Security Council encouraged naval forces operating off Somalia to take action against suspected piracy. Pirate attacks against aid ships have hindered U.N. 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.