Fans were seen clashing with stewards in the moments following Celtic's first goal in a match the Scottish champions won 2-1.
There were also reports claiming travelling supporters had ripped up seats and thrown them at fans sitting in the home sections.
While Police Scotland confirmed no Dutch fans were arrested during the game, UEFA has now decided to take action and a hearing will take place next month.
A spokesman said: "Disciplinary proceedings have been opened against AFC Ajax for crowd disturbances and throwing of objects (article 16 of the UEFA Disciplinary Regulations) at last night's UEFA Champions League match in Glasgow against Celtic FC.
"The case will be dealt with by the UEFA Control and Disciplinary Body on 21 November."
Celtic fans took to Twitter after the game to express their disgust at the actions of the Ajax supporters.
Supporter Colm O'Muiri posted: "Shame that they have to charge the club and cannot charge the fans aswell for throwing chairs #Ajax #Celtic."
Former Celtic winger Bobby Petta, who scored against his compatriots when the Hoops took on Ajax back in 2001, also went online to say: "Just got told ajax fans were attacking some celtic fans after the match !!! scandalous!!!!"