Capt Ciro Pinto said six pirates in a speedboat approached his ship, the Melody, and opened fire, but then fled after security men fired in the air.
He said his crew also sprayed water on the gunmen when they tried to climb aboard using a ladder.
Last year, pirates attacked more than 100 ships in the region, demanding huge ransoms for their release. Their attacks have intensified recently.
Capt Pinto told the BBC that the pirates tried to hijack his ship late on Saturday, about 290km (180 miles) north of Victoria in the Seychelles.
“One white small boat with six people on board approached the port [left] side of the ship and started shooting.”
The captain said the pirates fired some 200 rounds of shots on the vessel.
His said “our security started shooting in the air… and also we started spraying some water” to beat off the attackers.
Capt Pinto said the pirates were forced to give up after about five minutes of shooting and a high-speed chase.
The head of the Italy’s MSC Cruises, which owns the Melody, credited the captain for his “cool-headed” handling of the incident, Italy’s Ansa news agency reported.
The ship was on a cruise from South Africa to Italy. It was now headed as scheduled for the Jordanian port of Aqaba.
Somali pirates have hijacked about a dozen ships since the start of April, despite the presence of around 20 foreign naval vessels in the area.
International warships have been patrolling the waters off Somalia and in the Gulf of Aden in recent months as part of an effort to counter piracy.
They have freed a number of ships, but attacks have continued.
Somalia has been without an effective administration since 1991, fuelling the lawlessness which has allowed piracy to thrive.
Shipping companies last year handed over about $80m (£54m) in ransom payments to the gangs.
Taken from www.bbc.com
I think that someone actually needs to do something about the pirates- giving ships passing through the area protection with PT boats or something, – because they are fast and relatively cheap to buy, or just station soldiers on every boat like the Melody so that they can protect passengers if pirates attack.Also, if something like this is not done quickly, many people could be injured or held to ransom, bankrupting families when the victim could be already dead.