The SPCA said the video had been referred to its Inspectorate.
"The SPCA is disappointed to see such deliberate animal cruelty inflicted on a possum. Punching a stunned possum in the face is not pest control," a spokeswoman said.
Safe campaigns manager Marianne Macdonald said while possums were an introduced species, they still deserved respect.
While "there are calls for possum numbers to be controlled, these are sentient creatures - able to feel pain and distress, just like beloved cats and dogs at home," she said.
"They need to be treated with respect, not violence.
"Also, the humour from those witnessing this act demonstrates a toxic attitude towards animals, that is sadly very prevalent in some parts of our society and needs to be widely condemned."
Paw Justice spokesman Craig Dunn said while possums were classified a pest in New Zealand, they were a protected species in Australia.
"A classification does not and should not ever allow or encourage cruelty," he said.
"With councils around the country trying to bring in a pest category for cats, I believe we [are] going to see an increase in cruelty towards companion animals when we start labeling animals as pests."
Considered a pest, possums have a major impact on New Zealand's natural ecosystems.
Having prospered since being introduced from Australia, their population has exploded and predators, such as feral cats, have little effect in controlling their numbers, the Department of Conservation says.
While leaves remain the main part of their diet, possums are opportunistic omnivores, often competing with native birds and reptiles for other foods, such as fruit, berries and nectar.
"In 1993, possums were filmed eating the eggs and chicks of kōkako and this evidence changed many people's views of their threat to wildlife," DoC said.
"They eat invertebrates, including wētā, and are significant predators of New Zealand land snails such as Powelliphanta.
"They often occupy holes in tree trunks for their nests which would otherwise be used by nesting birds such as kākāriki and saddlebacks."
Dairy and deer farmers are also concerned at possums' ability to spread bovine tuberculosis.
"The value of economic loss in primary production for damage and control of possums is in the tens of millions," it said.