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The Wānaka Sun reported that the incident occurred on January 2, when a small group staged a protest outside the event.
A man, who had two children in his vehicle, allegedly stopped and screamed "I'm a Nazi, I'm a Nazi" at the protesters, while holding his arm in a Nazi salute.
Katherine Gollop, president of the Queenstown Vegan Society and spokeswoman for the protest group, said the man's acts were "very disturbing".
"He was laughing a lot and shouting random things at us. Then he lifted both hands off the wheel to put one across his face like Hitler's moustache, then one arm up in the salute, whilst screaming 'I'm a Nazi' at us," she told the Wānaka Sun.
"It just goes to show what kind of people go to rodeos and enjoy these types of events.
"Perhaps they go for personal attack because they have no rationally grounded argument in response to what we are doing."
Activists across the country regularly stage protests at rodeos, claiming that the events are cruel and do not belong in New Zealand.
That claim is strongly denied by the NZ Rodeo Cowboys Association, whose president Lyal Cocks told RNZ that protests were using "false information".
"We're most probably one of the most scrutinised sports in the equestrian area; we have animal welfare officers, we have vets at every rodeo, all our administrators and staff are working to make sure the rodeos run the best way they can, and we have the Ministry for Primary Industries involvement."