Five-year-old Staffordshire ridgeback-cross Wilco was in the passenger seat of the man's Chevrolet utility vehicle when it was left in park mode, with the engine running and handbrake off.
However, Wilco moved into the driver's seat and bumped the automatic column gear change into drive after its owner entered a nearby store on Tuesday.
The ute, which was parked about 8m from Fusee' Rouge Cafe, in the Cromwell Mall, rolled slowly forward into the building's glass-panelled bifold door.
The resulting damage was estimated at several thousand dollars.
While the dog's owner could have been charged, "that would not achieve anything", Sergeant Mike Williams, of Cromwell, said.
However, police are using the incident as an example of why animals or children should not be left in vehicles with engines running or keys left in ignitions.
"People just don't realise the sorts of things that can result," Senior Constable John Chambers, of Cromwell, said.
He said the cafe owner and dog's owner had insurance.
The door, which was buckled but did not break, would be examined to see whether it could be replaced in part or as a whole unit.
The cafe opened for business yesterday , although staff were kept busy fielding calls from people interested in the unusual incident.
Snr Const Chambers said the man responsible was "extremely embarrassed" and did not want to be identified.
"I think he's a bit like Wilco - with his tail between his legs," he said.
