The company has decided to pause all cruises in Australasia until May 31.
Regal Princess debut
It had planned to debut the 3,560-passenger Regal Princess in Sydney from December until April.
Regal Princess was to have joined her sister Royal-class ship Majestic Princess for a programme of voyages to New Zealand and the South Pacific.
Two Royal-class ships
SVP Asia Pacific Stuart Allison said it would have been the first time in history that Princess Cruises had deployed two Royal-class ships from the same homeport outside of Florida.
Five ships and 123 cruises
In all, there were plans for five Princess ships, with capacity for 13,790-passengers, to sail 123 cruises from six homeports Down Under in the 2020/21 season.
The company said the pause has been caused by the uncertainty of when international travel restrictions will be lifted.
Credits or refunds
Passengers will receive a refundable future cruise credit of 100% of the fare paid, plus a non-refundable bonus equal to 25% of the fare.
Alternatively, they have until November 30 to request a full refund.
Travel agent commissions for cancelled cruises that were paid in full have been protected.