Although most of the port's tourist areas have not been affected, parts of the Yarra Valley wine region and Healesville Wildlife Sanctuary have been hit, forcing Holland America to cancel Wildlife and Wineries tours when Rotterdam visited on Friday.
P&O Cruises' Arcadia is due to call in Melbourne this week, but officials have confirmed that there are currently no plans to cancel shore excursions.
Efforts to reach a representative from Princess Cruises, which also has a ship scheduled to visit the port this week, have not been immediately successful.
The Associated Press reported that a suspect, charged with setting one of the fires -- which killed at least 20 people near Churchill -- was taken into custody Friday.
So far, the death toll totals more than 180 people, and more than 7,000 have been left homeless. Thousands of animals have also perished in the blazes.