The owner of a dog shot and killed by police after it attacked other canines and people in a Sunshine Coast caravan park could face fines in the tens of thousands of dollars.

Police say they were called to a caravan park on Parkyn Parade in Mooloolaba just before 2:00pm on Friday with reports the dog had killed another canine and injured two others.

One man had tried to subdue the dog, which police said was a pitbull breed, with a shovel, but it continued acting aggressively.

A male officer fired three shots at short range at the animal before it died.

The dog was not wearing a collar or tag, but council officers were able to scan the body and identify the owner.

Sunshine Coast councillor Jenny McKay said the dog "has been known to the council".

"It was in our pound a couple of weeks ago," Cr McKay said.

"We will be fully investigating the matter."

Cr McKay said previous dog attacks in the region have been taken to court, attracting fines in the "tens of thousands of dollars" for owners.

"If the dogs are not doing the right thing it's the owner that's responsible," she said.

"It's against the local law to have dog off lead out of your control and that's where we will stand."