He was taken to hospital in Innsbruck after the accident, in which nobody else was hurt.
The prince, 43, is the second son of Queen Beatrix of the Netherlands.
However, he is not in line for the throne since marrying in 2004 without the government's permission.
Queen Beatrix and the prince's wife, Mabel, have been to visit him at Innsbruck's University Hospital, as have his brothers, Crown Prince Willem-Alexander and Prince Constantijn.
A friend of the prince who was skiing with him at the time of the avalanche has been questioned by police.
'Heart attack' He had been skiing with between one and three other people off the marked pistes when the avalanche hit shortly after midday local time last Friday, said resort officials.
He was buried by an avalanche reportedly measuring about 30m (yds) wide by 40m long.
A beeper he was wearing allowed rescuers to locate him quickly.
Speaking to reporters in Innsbruck, Dr Wolfgang Koller said it had taken nearly 50 minutes to revive the prince.
MRI scans have shown his brain suffered "massive damage'' in the avalanche.
The prince will be moved at a later date to a private clinic for further treatment but it may take years before he awakens, if ever, the doctor said.
The doctor explained that the prince's brain had been deprived of oxygen due to the amount of time spent under the snow.
"This resulted in a heart attack that lasted about 50 minutes....
"Fifty minutes of reanimation is very, very long, one might even say too long.
"Our hope was that the patient's mild hypothermia would provide some protection for the brain. This hope was not realised."
The Dutch royal family regularly spends skiing holidays in Lech, in the western Vorarlberg province of Austria.
Florian Moosbrugger, owner of the hotel where the royal family stays, had been skiing with the prince, a childhood friend.
He survived the incident unscathed, having worn an avalanche airbag, and reportedly dug his friend out with his own hands and called the emergency services, the Austrian Times reports.
He has been questioned by police seeking to establish which of the skiers went down the slope first, and how the avalanche began.
Mr Moosbrugger, who could reportedly face charges of "unintentional grievous bodily harm in particularly dangerous circumstances", says he is totally innocent.
According to his mother Kristl, Queen Beatrix herself comforted him after he was questioned.
Kristl Moosbrugger has defended her son.
"No avalanche was coming downhill," she told Austrian broadcaster ORF. "There were also strong skiing traces in the snow. They felt sure."
AnalysisThe Dutch royal family is held in high regard by the majority of people here in the Netherlands. Queen's Day is one of the most widely celebrated national holidays.
The news of Prince Friso's condition has been greeted with outpourings of grief and sympathy. Prime Minister Mark Rutte's office said he called Queen Beatrix on Friday morning to tell them the "country sympathises deeply with the royal family in this time of concern and grief".
As soon as the news broke, Prince Friso became a trending topic on the social networking site Twitter with users expressing their love and support for his wife, Mabel, and their two young daughters, Luana and Zaria. Queen Beatrix has said that the family has been moved by the "countless" messages of condolence and encouragement they have received.