A spokeswoman said the animal was shot about six weeks ago, but the owners thought it had a grass seed lodged in its chest.
It was not until the Birman cat fell seriously ill and the owners took it to the vet that they discovered it had a punctured lung caused by a small projectile pellet.
Chief inspector Amanda Swift was dismayed at the act.
“We have begun investigations to track the cause of this callous incident,” she said.
She urged residents who may have seen anything in Craigie about six weeks ago that could help the investigation to call the RSPCA on 1300 278 358.