Mr Luxon is attending his first international gathering of leaders on Tuesday after accepting an invitation from Australian Prime Minister Anthony Albanese.
However, his plans to take a NZDF 757 from Wellington airport went awry when maintenance issues grounded the plane.
Radio NZ reports Mr Luxon scrambled to get from the Rongotai defence force base to Wellington airport, where he caught an Air New Zealand flight to Auckland before transferring to a trans-Tasman flight to the Victorian capital.
The delay means the Kiwi prime minister will miss a few of his bilateral meetings at the summit, where he is meeting southeast Asian leaders back-to-back all day.
A number of accompanying staff and media were left at Rongotai base, hoping to attend the Melbourne talks if the plane is deemed flight-worthy.
The recurrent faults is an ongoing issue for New Zealand leaders, which Mr Luxon has previously labelled "incredibly embarrassing".
Unlike the Australian prime minister, who has a similar plane at his disposal, New Zealand leaders must borrow the plane from NZDF duty when they seek to undertake international travel.
The unreliability of the planes has led to prime ministers and ministerial delegations being stranded in various places around the world, including Melbourne, Townsville, Vanuatu, Solomon Islands and Washington DC.
The planes are due to be replaced by the end of the decade.
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