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One of the animals, which were grazing at the Dunedin Meditation Centre in Barnes Dr, had to be shot by police because of its injuries.
Another was treated by a vet.
Centre staff member Porntip Nartapan said two other alpacas in the paddock were unharmed.
The animals were on loan from Andy Nailard, from Flagstaff Alpacas.
The alarm was raised by a member of the public.
Ms Nartapan said she saw a squat black dog with a white chest run away from the scene.
The dog, which was wearing a collar, had not been located last night.
Police appealed for anyone with any information to contact them.
Dunedin City Council animal control officer Jim Pryde said even though the dog was described as a smaller "Staffie-like" dog, and alpacas were relatively large, all dogs could potentially attack stock.
Mr Nailard said he was waiting on advice from the police and animal control before deciding if the two uninjured alpacas should remain at the centre.
Putting down the badly injured animal had been the right decision.
The dead alpaca was a valuable female, but he was not angry at the dog's owners as "these things happen sometimes".
The injured animal had had a leg wound stitched amd was recovering, Mr Nailard said.