The sheep was taken to Chapel Street Vets where it was put down.
Mrs Gibson said as well as similar incidents involving sheep, there have been instances where people have been shooting birds. "Last time it was a majestic hawk, that the vet was unable to save," she said.
She said the incidents were "disgusting" and advised dog owners to keep an eye on their dogs at all times.
Masterton District Council spokesman Sam Rossiter-Stead said the council wasn't aware of this incident, but when contacted it would conduct an investigation to locate the offending animals and identify the owner.
Wairarapa police Sergeant Mike Sutton encouraged people to advise police of any similar incidents.
Masterton Motorplex co-ordinator Bob Wilton said it doesn't have sheep grazing on the land, so was unsure where the sheep might have come from.
Mrs Gibson said the owner of the ram could retrieve its carcass from the vet.