Qantas has been liaising with Boeing and safety regulators in Australia on an issue affecting some of the worldwide fleet of new-generation 737s.
Aircraft that have completed more than 30,000 takeoffs and landings (or cycles) required immediate inspections.
The airline said none of its 737s has reached 30,000 cycles.
Aircraft with more than 22,600 cycles require inspection within the next 1000 cycles.
''On Wednesday we advised that we had found one example of cracking in an aircraft with 27,000 cycles and this aircraft has been removed from service for repair. We'll provide a further update when the checks are complete,'' said the spokesman.
Safety regulators require inspections of the forks which hold up the wings on 737s to be completed over the next seven months but that process has been accelerated.
The Australian Licensed Aircraft Engineers Association (ALAEA) is calling for the airline to ground its entire fleet of 737s, some of which fly across the Tasman.
READ MORE:
• Premium - American Airlines' big NZ push: What's behind it
• American Airlines' big New Zealand move - Auckland to Dallas, Christchurch to LA
• Three of world's biggest airlines admit 'disturbing' seat cameras
• Premium - United Airlines tools up with new Dreamliner to Auckland as American Airlines expansion looms
The union's federal secretary Steve Purvinas said the aircraft should be kept "safe on the ground" until all 737s were inspected.
"Qantas are flying these planes, some have cracks and some do not," he told news.com.au. "But they don't know which ones don't."
But the airline has hit back.
''Qantas rejects the alarmist claims made by the licensed engineers' union, which are irresponsible and completely inconsistent with advice from regulators and the manufacturer.''
Boeing said on October 11 that 38 planes worldwide were discovered with pickle fork cracks and grounded for repair.
There are more than 6300 of the planes around the world and they are a different model to the Boeing 737MAX which has been grounded worldwide after two crashes in the past year.