The cruise company claims the man, who was in his eighties, intentionally went overboard.
They also expressed their condolences to the man's family.
'Our thoughts and prayers are with the man's family and friends in this very tragic circumstance,' a Carnival Australia statement said.
The 12-day cruise departed Fremantle in Western Australia six days ago.
The 80-year-old man went missing at 1.30pm shortly after the cruise left Indonesia, approximately 100 nautical miles south-east of Singapore.
A Perth local tweeted about the search and rescue mission.
'Fast rescue vessel just launched from the Sun Princess. Capt has arrived back at point where man overboard. Ship will now do a square search pattern to starboard,' they shared.
The tragic news comes just one month after Brisbane mum Natasha Schoefield went overboard from the deck of the Pacific Dawn cruise ship.
If you’ve been affected by the issues raised in this story, help is available from Lifeline on 13 11 14.