A reader told the New Zealand Herald the plane experienced a "massive lightning strike" and an engineering crew was sent from Auckland to assess and repair damage.
The Aviation Herald said the plane landed safely but scorch marks were visible on the fuselage. The Dreamliner only left Perth following repairs and the arrival of spare parts.
"Lightning strikes are not uncommon and aircraft are designed with this in mind," Air New Zealand said, without specifying the frequency of strikes.
Scientific American said on average, lightning hit each airliner in US service once a year.
"Lightning hits one part of the airplane, follows the outer surface of the frame and jumps back into the air, possibly leaving small burn marks where it enters and leaves," the Washington Post reported.
"If you're on a Dreamliner or another plane with a skin made mostly of composite materials, conducting material embedded in the composite does the same job as the aluminum skin of older aircraft."
The incident comes a month after trailblazing Air New Zealand pilot Captain Ann Barbarich died of a suspected brain aneurysm shortly after landing a Dreamliner in Perth.