Officers were called to Yallambee Lodge in Cooma after reports that 95-year-old Clare Nowland was carrying a knife.
The early morning incident has sparked outcry, over what advocates say was a disproportionate response.
The New South Wales (NSW) police chief has said she shares community concerns, and an investigation is under way.
Ms Nowland was found "armed" with a steak knife in the early hours of Wednesday morning, Assistant Police Commissioner Peter Cotter told media on Friday.
Two officers and care home staff tried to de-escalate the situation, before she began approaching police - "it is fair to say at a slow pace" - and was Tasered.
"She had a walking frame. But she had a knife," he said.
Family friend Andrew Thaler claimed Ms Nowland was struck twice - in the chest and the back - before she fell, suffering a fractured skull and a serious brain bleed.
Her family are already grieving as they do not expect her to survive, he told the BBC.
"The family are shocked, they're confused... and the community is outraged."
"How can this happen? How do you explain this level of force? It's absurd."
Community groups, including the NSW Council for Civil Liberties and People with Disability Australia (PwD), have criticised the police response.
"She's either one hell of an agile, fit, fast and intimidating 95-year-old woman, or there's a very poor lack of judgement [from] those police officers," PwD President Nicole Lee told the Australian Broadcasting Corporation (ABC).
"She needed somebody to... handle her with compassion and time, and not Tasers."
NSW Police has launched a critical incident investigation, which Commissioner Karen Webb said is being treated with "the utmost seriousness".
"I understand and share the community concerns," she said.
The officer involved has not been suspended, but will be interviewed as part of the investigation, which will include the homicide squad.
"No officer, not one of us, is above the law," Mr Cotter said.
"All our actions will be scrutinised robustly from a criminal perspective as well."
The care home, which is run by the Snowy Monaro Regional Council, has defended its response. The staff followed procedures and did what was needed in the circumstances, the council's chief operating officer Jeff Morgan told local media.
Yallambee Lodge opened in 1995 and looks after residents with "higher needs", according to its website.
Ms Nowland has lived at the home for more than five years, the ABC reported.
The great-grandmother is well known locally, and appeared on TV in 2008 to mark her 80th birthday by sky-diving over Canberra.
-- Courtesy of BBC News