The navy says the USS Nicholas came under fire early Thursday (12:27am local time) while operating west of the Seychelles islands, in the western Indian Ocean.
It says personnel from the navy ship disabled the pirate boat, and detained three suspects before sinking their vessel. Two more suspected pirates were captured on the mother ship.
Officials say the suspects will remain in U.S. custody on board the Nicholas for the time being.
Naval forces from the U.S., European Union, and other world powers are patrolling the waters off East Africa in an effort to stop Somali pirate attacks.
The pirates have hijacked dozens of ships for ransom during the past few years.
Maritime authorities have warned commercial vessels to be extra-vigilant of attacks because of clear weather in the region