The Parkhead club were stunned yesterday after Brown received a three-match suspension for kicking out at Brazilian midfielder Neymar during this month's 1-0 Champions League defeat to Barcelona.
That means he will miss all but the final game in Group H this season. Neil Lennon will appeal the decision, but it is believed that such a move could see the ban increased.
Brown was sent off for aiming a kick at Neymar, an offence which was widely expected to earn an automatic one-game suspension.
However, Uefa's disciplinary panel have viewed the incident as assault - an offence which carries a three-match ban.
And while Celtic can appeal the suspension, a spokeperson for Uefa revealed that if they are unsuccessful the punishment could be cranked up even further.
"If a club decides to appeal then the decision can be to reduce the punishment, keep it the same or even increase it," he said.
"The disciplinary panel have looked at the incident and decided that it should be bracketed as assault.
"The sanction for that begins with a minimum of a three-game ban."
The judgment is a serious blow to Celtic's chances of overcoming defeats in their opening two group games and qualifying for the Champions League knockout stages for a second season running.
Lennon already has fitness doubts over winger Derk Boerrigter and defender Mikael Lustig for the visit of the Dutch champions, while Adam Matthews and Steven Mouyokolo are long-term absentees.
Speaking immediately after the October 1 match at Parkhead, Lennon had said: "I think it is very soft. If there was any contact, it was minimal. There was a lot more in a game that warranted heavier punishment."
In a statement last night, the Parkhead side said: "Celtic can confirm that they have received notification from Uefa of the sanction. The club finds this to be excessive and they will be appealing against the decision."