Victoria Police said they were called to an address on Ancona Drive after reports a man, in his 60s, had been attacked by a dog.
"Upon attending the address, officers located a deceased man and a woman with serious injuries," the police said in a statement, according to news.com.au.
"Shots were fired by members to deter the dog from further attacking the woman and members and it was contained in the premises."
A neighbour told the Herald Sun he tried to spray the dog with water to distract it after he heard screams.
"There was no stopping it. It's a giant pit bull," he said.
There are reports the deceased man had been recovering from an operation and was in a motorised wheelchair.
A neighbour told The Ageshe would frequently chat with the victim at the supermarket.
"He's been a very lovely person. We will miss him a lot, especially my husband. We love him," she said.
A woman in her 60s was also injured in the mauling, police said. She was taken to the Royal Melbourne Hospital for treatment where she is thought to be in a stable condition with severe injuries to her upper body.
Efforts to capture the dog proved futile until a ranger eventually subdued it about 10.30pm. It is being held by Whittlesea Council.
Senior Sergeant Glenn Parker said the dead man's daughter-in-law gave consent to destroy the animal.
"The dog belongs to the occupant's son, the dog's been here for quite some time," he told reporters at the scene.
"He (the dog) will be taken to a veterinarian, and my understanding is that the owner of the dog has actually consented to that dog being put down," Sgt Parker said.
"It's an older dog, it's quite familiar with all of the members of the family and my understanding is it's out of character for the dog."
RSPCA Victoria's Tegan McPherson said there were several causes of dog attacks, but breed wasn't necessarily one of them.
"From what we're hearing, this dog didn't necessarily have a background of aggressive behaviour until this incident," Ms McPherson told ABC Radio.
Triggers for dog attacks could range from environmental factors to pain and fear, she said.
"Without understanding the context of this particular incident, it could be fear related, it could be something else going on in the environment or it could be related to pathological changes in the dog's brain or related to pain," she said.