The move is seen as part of Ukraine's efforts to reinforce its army as soldiers struggle to hold positions against Russia
Boeing had previously reported a problem with the model's "pickle fork" - a part which helps bind the wing to the fuselage - prompting US regulators to order immediate inspections of aircraft that had seen heavy use.
A company spokesperson on Thursday told AFP that so far around 1,000 planes worldwide had "reached the inspection threshold", with less than five percent - or up to 50 jets globally - having "findings" that kept them grounded until repair.
Qantas grounds Boeing 737 plane
The grounding is the latest safety concern for Boeing, as it reels from two 737 Max crashes that killed 346 people and highlighted problems with the planes' flight handling software.
The US aviation authority this month ordered checks of Boeing 737NG planes that had flown more than 30,000 times.
That came after the company reported the "pickle fork", which helps connect the wing to the fuselage, could be prone to cracking.
Qantas said Thursday it had found the fault in a more lightly used aircraft, one that had recorded fewer than 27,000 flights.
"This aircraft has been removed from service for repair," Qantas said in a statement, adding it had hastened its inspections of 32 other 737NG plans to be completed by Friday.
The announcement by Qantas raised fears the cracking issue could affect newer planes than previously thought, leading to calls for the Australian airline to ground its entire 737 fleet.
"These aircraft should be kept safe on the ground until urgent inspections are completed," an engineers' union representative, Steve Purvinas, said in a statement.
However Qantas described the call to ground its 737 fleet as "completely irresponsible".
"We would never operate an aircraft unless it was completely safe to do so," Qantas head of engineering Chris Snook said.
"Even when a crack is present, it does not immediately compromise the safety of the aircraft."
The FAA initially said Boeing notified the agency of the problem after encountering the issue on a plane in China and that subsequent inspections showed other planes also had cracks.
The NG is a precursor plane to the Boeing 737 Max, which has been grounded since mid-March following the two deadly crashes in Indonesia and Ethiopia.
Boeing chief executive Dennis Muilenburg faced another round of tough questions on Wednesday from US lawmakers who accused the company of a "lack of candour" over the crashes.
The move is seen as part of Ukraine's efforts to reinforce its army as soldiers struggle to hold positions against Russia
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