The 'Grand Princess' cruise ship has been on an 18-day round trip to Queensland and back.
It is unclear how many people on board are affected, but the ship has capacity for 2600 passengers and 1150 crew members.
South Australian premier Peter Malinauskas said those on board needing urgent care would be transported to hospital facilities in a way that was safe.
"It's been something we've been monitoring pretty closely over the last 48 hours," Mr Malinauskas told Nine's Today show on Monday.
"The good news is that reports that we've got from the cruise operators that the number of cases presenting has actually dramatically decreased over the course of the last couple of days."
SA Health says it's up to the cruise ship operator to manage outbreaks on board, and at this stage it seems there are very few cases on board.
In a statement, SA Health confirmed the ship docked in Melbourne on Saturday to undergo a clean, and all passengers disembarked while that was undertaken.
"As with all cruises, operators are responsible for having processes in place to manage outbreaks of communicable disease," the statement said.
Cruise operator, Princess Cruises has been contacted for comment.
e
8°C