The Viking Orion is being cleaned by divers about 12 nautical miles off the coast of the SA town of Victor Harbor on Sunday.
The luxury vessel hasn't docked since casting off from Wellington in New Zealand on Boxing Day, according to ship-tracking website VesselFinder.com.
It was reportedly denied permission to dock in Christchurch, Dunedin and Hobart before setting course for Adelaide.
Before it could arrive there, Australia's National Maritime Coordination Centre established that the ship had small amounts of biofoul - marine microorganisms, plants, algae, or small animals - on its hull.
Authorities then ordered the Viking Orion's agent to have its hull cleaned before entering Australian waters.
"The vessel is required to undergo hull cleaning to remove the biofoul and prevent potentially harmful marine organisms being transported by the vessel," the federal fisheries department told AAP in a statement on Sunday.
"Professional divers were engaged directly by the vessel line/agent to clean the hull while at anchor outside Australian waters.
"The management of biofoul is a common practice for all arriving international vessels."
A Viking representative said after the hull is cleaned, the Orion will set sail for Melbourne on Sunday and resume its itinerary by Monday.
"A limited amount of standard marine growth is being cleaned from the ship's hull - a standard cleaning procedure for nautical vessels," they told AAP in a statement on Sunday.
"While the ship needed to miss several stops on this itinerary in order for the required cleaning to be conducted, she is expected to sail for Melbourne as planned on January 1, and we are expecting the scheduled itinerary to resume completely by January 2.
"Viking is working directly with guests on compensation for the impact to their voyage."
The ship's Master Marko Snajdar wrote a letter to passengers on Friday apologising for the situation which was screened on multiple TV news channels.
"We acknowledge that the current cruise falls short of your expectations. Immediately upon your return a member of our Customer Relations team will contact you with an adjusted offer of compensation," he wrote.
"Viking is interested in keeping you as lifetime travellers, and we hope to see you under less exceptional circumstances on one of our ships in the future."
