The guided missile destroyer USS Winston S Churchill went in pursuit of a suspect vessel after receiving a report of piracy, the navy said.
When other efforts failed, the Churchill fired warning shots to bring the boat to a halt.
There have been numerous attacks by pirates off Somalia, some of the most dangerous waters in the world.
The US navy's Fifth Fleet, which is based in Bahrain and patrols the Indian Ocean, received reports of "an attempted act of piracy" approximately 50 miles (80km) off the Somali coast on Friday, it said in a statement.
No government
The Churchill shadowed the suspect vessel, and tried to make contact over the radio, before resorting on Saturday to "aggressive manoeuvring in an attempt to stop the vessel".
When this failed, "Churchill fired warning shots. The vessel cut speed and went dead in the water," the statements said.
Later an unspecified number of sailors were taken off the vessel and a quantity of small arms was recovered, the navy said.
Piracy, including hijackings and hostage-taking, has become common off anarchic Somalia, where there has been no effective central government since 1991.
An attack late last year against a luxury cruise liner was repelled by an ear-splitting acoustic device.
Shipping companies say there have been 35 incidents of piracy off the Indian Ocean coast of Somalia in the past nine months.
The transitional Somali government has signed a $50m (£28m) two-year deal with a private US marine security company to carry out coastal patrols.
However, it is not clear where this money would come from, as the government has not effectively taken office. The security company has not started work.
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