Two small boats approached the 30,277 tonne Nautica, which was carrying 684 passengers though the Gulf of Aden, in the Arabian Sea, in an area known as "Pirate Alley".
As the cruise ship began evasive manoeuvres, eight shots were fired from one of the skiffs.
None of the shots hit the ship.
The pirates got within 300m of the liner but were unable to keep pace with it.
The incident comes two weeks after Somali pirates seized Sirius Star, a Saudi tanker carrying oil worth $US100 million.
Craig Harris, of Auckland, chairman of Cruise NZ, which markets New Zealand as a cruise-ship destination, confirmed Nautica was sailing to New Zealand and would arrive in Dunedin on January 16.
The attack illustrated the boldness of the pirates, who were prepared to take on a cruise ship carrying 684 passengers, he said.
While reports of piracy in the area had increased 75% this year, "cruise ships are conscious of the piracy risk and have a number of devices that other ships don't have", he said.
One was a long-range acoustic device capable of "blowing the eardrums" of a pirate within 2km, Mr Harris said.
The latest incident was the second time a cruise ship had come under fire off Somalia in recent years - Seabourn Spirit was shot at by pirates armed with machine guns and rocket-propelled grenades there in 2005.
Mr Harris said that by coincidence, both cruise ships were heading to New Zealand as part of their voyage.
Only 5% of cruise ships came to New Zealand via the Suez Canal from the Mediterranean.
Oceania Cruises, which operates Nautica, said in a statement no-one on board was harmed.
"All requisite international authorities have been notified and all anti-piracy precautions were in place prior to the event."
Nautica was due to arrive in Salalah, Oman, yesterday, before sailing to Singapore.
