Travelling fans were seen clashing with stewards in the moments following Celtic's first goal in a match the Scottish champions won 2-1, while reports claimed that seats were ripped up and thrown.
Police Scotland confirmed no Dutch fans were arrested during the game but UEFA has 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 travel to the Netherlands for the return fixture at Amsterdam Arena on 6 November.