Dutch police claim that they made 15 arrests in the centre of Amsterdam prior to the Hoops' 1-0 defeat to the Eerste Divisie outfit.
The authorities have alleged that a "large group of Celtic supporters" attacked plain-clothed police officers unprovoked.
The majority of those arrested are said to have been Celtic fans, but supporters of other clubs were also reportedly involved.
"At the end of the afternoon a large group of Celtic supporters attacked police officers in plain clothes," said a police spokesman.
"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."
Lasse Schone scored the only goal of the game to give Ajax maximum points.