Public health director professor Mark Ferson said a small number of crew also contracted the norovirus type bug.
"The ship has instituted maximum control measures, including increased sanitation, and further cleaning and hygiene procedures will occur prior to passengers arriving on board this afternoon. Incoming passengers will be advised by the ship of the outbreak and about recommended hygiene measures," he said.
The ship's swimming pool was drained and all food buffets were closed to combat the spread of the virus.
This ship docked in Circular Quay after a 12-day sailing around New Zealand.
News media reported a small number of passengers did not report their symptoms days earlier which may have led to the outbreak.
Health officials said no passengers or crew were admitted to hospital.
"There have been no medical disembarkations or patients requiring hospitalisation," professor Ferson said.
A Carnival Australia statement said: "In the closing few days of the cruise a small proportion of the total number of passengers on board reported gastro intestinal symptoms confirmed as being due to the common stomach bug norovirus."
Air Ambulance and cruise ships