The Dutch champions face disciplinary sanctions following the incidents at Parkhead where travelling fans threw objects at law enforcement officials
A number of travelling fans were photographed ripping out seats before hurling them at police officers stationed inside Parkhead.
One steward reportedly sustained injuries after being struck by a plastic chair thrown from the Ajax section and a Uefa spokesperson announced on Wednesday that disciplinary proceedings had already begun.
"Disciplinary proceedings have been opened against Ajax for crowd disturbances and throwing of objects [article 16 of the Uefa Disciplinary Regulations] at last night's Champions League match in Glasgow against Celtic.
"The case will be dealt with by the Uefa Control and Disciplinary Body on November 21."
Police Scotland confirmed that no arrests had been made following the incidents, but took to Twitter to announce that they would also launch an investigation into the scenes.
They wrote: "A full investigation is being carried out into the behaviour of a number of Dutch supporters.
"Our officers are reviewing CCTV images. Any info gleaned will be shared with our Dutch counterparts to identify those involved."
Some 3,000 Ajax supporters were estimated to have made the journey to Glasgow.
Both teams will meet again in Amsterdam for the return fixture on November 6.