The man was taken to hospital after being injured trying to jump a barrier to get onto the ground where the Kiwis were knocked out of the Rugby League World Cup by Fiji, police said in a statement.
The Fijians dominated much of the game, restricting the Kiwis for field position in a game where defences were on top throughout.
Apisai Koroisau kicked penalties either side of half time at Wellington Regional Stadium to give Fiji victory in a dogfight of a test match and a ticket to a semi-final against reigning champions Australia in Brisbane next week.
Two other people were arrested during the game.
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Shaun Johnson levelled before Taane Milne scored the decisive points with another penalty after 62 minutes.
Fiji's defence, largely untested during an unbeaten pool run, was never really pressured in the first 40 minutes, the Kiwis their own worst enemies with a succession of handling errors and missed tackles.
However, Fiji came back from the kick-off with phenomenal defence and as Kevin Naiqama returned the ball with intent, he passed to Suliasi Vunivalu who drew a professional foul from Jordan Rapana - the winger sent to the sin-bin by referee Matt Cecchin.
The Kiwis were ousted from the tournament after a 4-2 quarter-final defeat at the hands of Fiji on Saturday night.