Ms Jones said the injuries were not recent and had become infected.
Ms Jones said the cat, dubbed Apollo by SPCA staff, might need specialist surgery to save its leg, and it could be safer to leave the pellets where they were.
SPCA Auckland chief executive Christine Kalin described the case as severe.
"I don't see how someone can do that to an animal," Ms Kalin said.
"As the frontline organisation for animal welfare, we do often have cases where horrific things have happened. In terms of severity, this is on the upper end of severity.
"One of our warrant inspectors is currently investigating the incident as this is a clear breach of the Animal Welfare Act and we would like to be able to identify the person that committed this dreadful and horrific act to ensure that they are held accountable."
Massey Archery Club president Mary Thomas said the club was trying to identify where the arrow came from.
"We've seen the arrow and photos of the cat, and we believe that arrow was not shot with the bow that it was made for.
"What we think has happened is that someone has overshot a target and not been able to find their bow and that someone else has picked it up and mucked around with it," she said.
The club had made a donation towards the costs of treating the cat.
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