Instead, the 53-year-old is heading to Melbourne on Tuesday to attend his daughter Olivia's university graduation.
"I think family is really important and I don't make any apologies for doing it," he said from Wellington on Monday.
"I would expect others in my cabinet to take decisions that support their family life as well."
Ms Luxon's LinkedIn states she is studying a Bachelor of Arts at the University of Melbourne, majoring in criminology and sociology.
Mr Luxon, who took office a fortnight ago, will miss a day in parliament, handing over the reins to Deputy Prime Minister Winston Peters, who will act in his place for the day.
It is not the first time that Mr Peters will be acting prime minister, having served as deputy in two previous governments.
The 78-year-old has courted controversy on a near daily basis since his latest return to government, serving it up to media, which he baselessly accuses of taking bribes by accepting public funding.
Last week, Mr Peters incorrectly stated the indigenous people of the Chatham Islands - the Moriori - had died out in 1936.
However, recent census data shows several hundred people self-identify as Moriori, with the New Zealand government settling a treaty claim with the group in 2021 for historical wrongdoing.
"It is time to move on from this narrative," Moriori man Maui Solomon told NZ media outlet Stuff.
"I have been spending 40 years of my life battling to have the truth told about Moriori."
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