A search is underway off Australia for a couple who fell overboard into shark-infested waters from a cruise ship returning to Sydney from a Pacific tour.

The 30-year-old man and 27-year-old woman were reported missing from the Carnival Spirit liner after it docked at Circular Quay in Sydney on Thursday morning.

"We have determined that two people have gone over the side of the ship -- we believe they have gone overboard and we are searching for them," said Detective Superintendent Mark Hutchings, who said the pair were Australian.

After reviewing security footage on the ship, police said they believe the couple fell overboard just before 9pm on Wednesday (1100 GMT Wednesday) around 65 nautical miles off the coast, north of Sydney.

"It's game on and we're pulling out all the stops to try and locate them," said Hutchings, with ships and planes scouring an area of 520 nautical miles.

"As far as I'm concerned, we are searching for them in the hope they we find them alive. Conditions are not overly bad," he added.

Police said no lifejackets were missing from the ship.