The ship, which set off from Venice, Italy, eight days ago, suffered a 3.5-hour power outage Sunday as it cruised between Mykonos and Naples, Travel Weekly, a British trade publication, reported.
The cruise will end when the Royal Princess reaches Naples Tuesday evening.
Passengers will be offered a full refund, plus a 25 percent discount on future cruises.
"The ship's technical team continued to evaluate the problem overnight and, upon further assessment, it became apparent that repairs need to be made to fully resolve the situation," Princess Cruises said in a statement. "We sincerely regret this means the remainder of the current cruise will be cancelled, and passengers will disembark the ship in Naples."
The company said it was insure whether the Royal Princess will be able to make its next voyage.
"The impact of the repairs on the next Royal Princess cruise, scheduled to depart from Barcelona on September 27, is not yet known and we will keep passengers fully advised as details become known," Princess Cruises said. "Once again, we are deeply sorry for this unanticipated disruption of our passengers' vacation plans, and we appreciate their patience and understanding of these circumstances."