Quick thinking by police has likely saved a woman's life after her arm was severed by her own dog in a vicious attack.

Officers promptly applied a tourniquet after they found the woman, in her 30s, bleeding heavily outside a north Queensland residence with an aggressive dog barricaded inside.

The attack in Townsville came a day after a woman was critically injured by a dog in Melbourne.

Officers arrived at the Garbutt address about 7am on Friday and found the woman nursing a severed right forearm after being attacked by her dog, believed to be a large Pitbull cross.

The woman quickly received first aid from police before paramedics arrived, with the detached arm reportedly later found in a bid to have it reattached.

Applying the makeshift tourniquet "might have saved her life", Senior Sergeant Scott Warrick said.

After being rushed to Townsville University Hospital, the woman was reportedly in a serious but stable condition.

"Her blood loss was quite extensive, and that tourniquet has pretty much ceased that blood loss," Sgt Warrick told reporters.

"I commend them for their efforts under very high pressure situation.

Sgt Warrick said it was one of the most significant injuries from an animal he had seen in his 37-year career.

"This is the first time I've gone to such serious injury as a result of a dog attack," he said.

"The injuries to this lady are just absolutely awful and we wish her a speedy recovery."

Police attempted to subdue the dog by trapping it inside the house.

"It was very angry, very aggressive...(it) was still trying to get outside," Sgt Warrick said.

The dog continued to be aggressive and had to be euthanised at the scene. 

"I have dogs, and to see an outcome like this is absolutely heartbreaking, and we do understand people will be upset," Sgt Warrick said.

"But we were left with no other choice...it was as humane as possible.

"What we did today is an absolute last resort."

Sgt Warrick said the dog had been subject to previous complaints of aggressive behaviour and another less serious attack several weeks ago.

(In the attack in Melbourne, a woman suffered severe injuries after being mauled by three dogs. (Joel Carrett/AAP PHOTOS)

Under laws introduced earlier this year, the owner of a dog that kills or seriously injures someone can be fined more than $100,000 or face three years in prison.

But Sgt Warrick said given the seriousness of the woman's injuries it was unlikely she would be charged.

The woman also owned a smaller dog, which is now in the care of the RSPCA.

In the Melbourne attack, a woman was critically injured, and the three dogs responsible were fatally shot by police.

She remained in a critical condition on Friday. 

Police tried to save her by using pepper spray on the dogs before drawing their guns.

"We are distressed about yesterday's incident and the injuries to one of our residents - we remain concerned about her welfare," Greater Dandenong City Council chief executive Jacqui Weatherill said in a statement.

It was also confirmed there had been numerous previous complaints and concerns from neighbours about the dogs.

"We have previously taken action in response to those concerns and visited the property," Ms Weatherill said.

By Savannah Meacham in Brisbane