Senior Sergeant Steve Aitken said the large brown dog, owned by a Sawyers Bay man, was hit by the patrol car, which was being driven towards Dunedin by a Port Chalmers police officer.
The dog had been secured by a chain in the back of a utility vehicle being driven in the opposite direction by the animal's owner.
''It appears the dog has somehow become disconnected from the chain securing it and jumped from the back of the ute, directly into the path of the police car,'' Snr Sgt Aitken said.
The dog died almost instantly and its owner was extremely upset, he said.
The patrol car was towed away for repair. The incident caused minor traffic disruptions.
Snr Sgt Aitken said no charges would be laid in relation to the incident.