Moira Shire Council's infrastructure general manager Andrew Close said since December 2019 there has been 14 separate reports in which people, livestock or other dogs were injured.
One was in Barmah and another was in Nathalia.
“In two of the more serious cases, a dog received a 7 cm gash which required emergency vet care and some livestock were mauled and sustained life-threatening injuries,” Mr Close said.
Dog owners are reminded that the adequate confinement of dogs requires secure escape-proof fencing, safe visitor access to the home's front door and securely shut gates.
“When owners are walking their dogs, it is also important to ensure the dog is securely tethered to a lead,” Mr Close said.
He said action would be taken in the event of any unprovoked animal attack.
“Council officers can, and will, if required, issue fines and infringement notices and can escalate the more serious cases to criminal charges,” he said.
Residents are encouraged to report to council immediately if they see any wandering dogs or have concerns about inadequately confined dogs, by phoning 5871 9222.