She was on the seventh night of a 12-night voyage when she experienced electricity problems.
Some 3,000 passengers and 1,336 crew were left with minimal power for 3.5 hours while she was sailing between Mykonos and Naples.
The backup generator was used to provide essential services including toilets during the outage.
Power was later restored and the ship continued to Naples.
A company statement said Royal Princess’ technical team evaluated the problem and determined that further repairs were needed to fully resolve the issue.
Passengers will be disembarked in the Naples and have been offered a full refund and a 25 percent future cruise discount.
The statement read: “Princess is making homeward air arrangements for passengers, and we anticipate that passengers will spend Tuesday night onboard and depart the ship on Wednesday.
“We have dispatched a care team to Naples to ensure that all our passengers are provided with any assistance they may require.”
Royal Princess was christened by a royal princess, the Duchess of Cambridge four months ago.
The power issue follows last month’s malfunction on board Sun Princess, which left 2,000 cruisers scrambling to find alternative means of travelling from Singapore to Freemantle, Australia.