Two boats carrying between eight and 10 pirates armed with machine guns and rocket-propelled grenade launchers attacked the "Spirit," which had 150 passengers and 160 crew members on board, CNN reported.
Canadian passenger Mike Rogers said, "the captain tried to run one of the boats over," and eventually outran the boats. The captain didn't hit the emergency alarm for fear passengers would rush to the deck. He alerted them over the loudspeaker.
One person was injured but there are no details.
The ship suffered a little damage. Rogers said there wasn't running water and he heard that a grenade went off in a cabin.
Seabourn Cruise Line President Deborah Natasohn said the ship was on its way to the Seychelles Islands.
She said the company would reevaluate whether it will continue voyages into the Somalia coastal area. The World Food Program announced Thursday that pirates are hijacking shipments into the area and hampering relief efforts.
The WFP website called the coastline "one of the most dangerous in the world."