The 20-year-old had "cardiac arrhythmias" - heart rhythm problems - during the game against Werder Bremen.
The club statement said the chances of recovery from the damage is nil.
It added: "The diagnosis was made that a lot of [his] brain is not functioning. All this probably occurred due to a lack of oxygen supply."
On Monday, the club had said tests showed his "heart is functioning normally" and brain scans did not detect "any anomalies" - but new tests revealed the extent of the damage.
The Amsterdam-born player was flown by helicopter to hospital in Austria - where the abandoned friendly match was being played.
Ajax say he will soon be transferred to a hospital in Amsterdam for further care.
Former Manchester United and Fulham goalkeeper Edwin van der Sar, now CEO at Ajax, said: "This is the worst possible message. It is terrible. We feel enormously for his parents, siblings and other relatives.
"The blow is also difficult for Ajax, though we knew we had to consider this scenario. They were uncertain days, lots of people in different ways have sympathised with his situation and is greatly appreciated.
"Abdelhak is such a great talent, but unfortunately we will never know how far his star would have reached had this not happened. "
Nouri played 15 league and cup games for Ajax in 2016-17, scoring one goal in a Dutch Cup tie.
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Ajax midfielder Abdelhak Nouri suffered "serious and permanent brain damage" after collapsing in a friendly match on Saturday.