They will remain in custody until November 21, when they will be brought back before a judge.
Twenty eight Scots were among 44 people arrested following the clashes on Wednesday which left eight Dutch police officers injured.
Dutch police said 22 of the Scots were released with fines of up to 500 euro (£417).
One officer was knocked unconscious in the fighting in Dam Square while others suffered broken noses.
Police said the majority of those arrested were Celtic supporters.
The Scottish club responded to claims from fans that they were poorly treated by opening an internal investigation and said that the club will be liaising with the local authorities in Amsterdam, Scottish police and the British Consulate in order to fully understand events.
A club statement read: ''We would stress that there is no excuse for any form of violent conduct.
''In addition, we have received numerous complaints from Celtic supporters in relation to their treatment in Amsterdam, which we will also investigate fully.
''There is no question that Celtic supporters have been subjected to a high degree of provocation.''
The incident came after clashes during Ajax's trip to Glasgow a fortnight ago, while it was also reported around 50 supporters were in the Old Sailor Cafe in Amsterdam when they were attacked by a group of masked men on Tuesday night.
''Last week, our supporters were the target of missiles being thrown from Ajax supporters at Celtic Park, a night where 300 seats were damaged within the stadium,'' the Celtic statement continued.
''This was followed up by an organised attack on a group of Celtic supporters in Amsterdam on Tuesday, the night before the match. We have also received numerous individual reports of other attacks on our fans.
''The Celtic travelling support has a magnificent reputation across Europe and our fans have visited major European cities over many years without incident.
''Once again the overwhelming majority of our supporters behaved impeccably.''
UEFA opened disciplinary proceedings against Ajax last month after the clashes with police and stewards at Parkhead during the initial fixture, which the home side won 2-1.
A disciplinary case is to be heard on November 21.