Eight police officers were injured in the violence in the city centre before kick-off yesterday.
Police said fans armed with bottles and sticks attacked plain-clothed officers in an incident described as "coming out of nowhere".
One officer was knocked unconscious in the fighting in Dam Square and police said the majority of those arrested were Celtic fans.
Eighteen of the 28 Scots remained in custody and may be released with a fine or brought before a magistrate, who will decide whether they should face further disciplinary action.
A police spokesman said: "At the end of the afternoon, a large group of Celtic supporters attacked police officers in plain clothes. Eight were injured and one was knocked unconscious.
"A few of them had broken noses and needed stitches above their eyebrows and on their lips.
"Bottles and sticks were used in the attack which came out of nowhere. 'There were 15 arrests, mostly Celtic supporters."
Celtic lost the match 1-0 and face an uphill battle to reach the knockout stages of the competition.
A Foreign Office spokesman said: "We are aware of the arrests of a number of British nationals in Amsterdam.
"We are liaising with the authorities and stand ready to provide consular assistance."
Before the match, Celtic urged fans in the city to be "extra vigilant" after a group of supporters were attacked in a city centre bar.
It was reported around 50 supporters were in the Old Sailor Cafe in the city when they were attacked by a group of masked men on Tuesday night.
There were no serious injuries and a number of people were arrested.
The attack follows trouble last month when a group of Ajax fans ripped up and threw seats at police and home fans as the teams played in Glasgow.
UEFA opened disciplinary proceedings against the Dutch club after the clashes with police and stewards at Parkhead during a match which the home side won 2-1.
A disciplinary case is to be heard on November 21.
The night before the match at Celtic Park, British Transport Police arrested two Dutch fans over alleged disorder in Glasgow Central train station.
Around 12,000 Celtic fans were expected in Holland for last night's match and the club said fans should not travel to the stadium unless they had a ticket for the Celtic section.
A spokeswoman for Police Scotland said: "As is normal practice during international tournaments, Police Scotland has deployed officers to Amsterdam for the Ajax v Celtic match, and we have been working closely with Dutch police and authorities in relation to security at this fixture.
"We have been made aware of some disorder in Amsterdam with a number of Celtic fans having been arrested.
"We will continue to work with our Dutch colleagues to identify anyone responsible for carrying out acts of disorder."