The 20-year-old collapsed during a pre-season friendly against Werder Bremen in Austria on Sunday when his heart stopped.
He was revived on the pitch and airlifted to hospital, but Ajax have confirmed that although his heart is working normally, he has lost function in parts of his brain.
"The chances of recovery of these crucial brain functions is nil," the club said in a statement on its official website (www.ajax.nl). "This was probably due to a lack of oxygen supply to his brain."
Nouri has been cleared to leave hospital in Innsbruck and will be transferred to Amsterdam in the coming days, Ajax said.
"This the worst possible news. It's terrible. We feel enormously for his parents, siblings and other relatives,” Ajax director Edwin van der Sar said. "Their suffering is impossible to describe.
"The blow is also being felt at Ajax, though we knew we had to consider this scenario. There were uncertain days, lots of people in different ways have sympathised with his situation. It is greatly appreciated.
"Abdelhak is such a great talent, but unfortunately we will never know how far his star would have reached had things not have happened like this."
Nouri made 15 appearances for the Dutch club last season, including three in the Europa League, though he did not play in the final, a defeat to Manchester United.
He is a Dutch youth international and was born in Amsterdam to parents of Moroccan descent.
The incident comes a little over a month after Ivory Coast international Cheick Tiote collapsed in training with Chinese club Beijing Enterprises and died on June 5.
(Reporting by Nick Said; Editing by Louise Ireland)
