The disturbances took place in the immediate aftermath of the Dutch's side's 2-1 defeat to the Hoops.
One seat appeared to land on a line of stewards and police officers that were dividing the two sets of opposing fans.
Another showed around six ripped-out seats lying behind police officers after the final whistle in the match.
It came after "instances of disorder" were dealt with by police in Glasgow ahead of the big match.
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."
Fans registered their disgust on Twitter.
One said: "Throwing seats, destroying Glasgow, trying to fight with Celtic supporters, just a disgrace to their club."
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!!!!"
A Police Scotland spokeswoman described the scenes as "minor disorder". They had no details of injuries.
Earlier Police Scotland confirmed that there had been some reports of unrest but were quick to reassure the public that officers had "quickly got the situation under control".
Social media websites were flooded with with reports of violence and rioting in the city centre and Glasgow's east end ahead of kick-off.
Superintendent Brian McInulty said: "This game has been sold out, with thousands of fans attending the match. The area is busy but is being policed appropriately.
"Officers have dealt with some instances of disorder, however the police response has been immediate and officers have quickly got the situation under control.
"We are experienced in dealing with major events and there is a significant policing operation in place to deal with any issues which may arise both at the ground and in the city."
On Monday a British Transport Police (BTP) officer was injured after a riot involving between 40 and 50 football fans in Glasgow's Central Station at around 10.45pm.
A 17-year-old male Dutch national was arrested and appeared at Glasgow Sheriff Court.
BTP said further arrests had been made and they were hunting other people in connection with the incident.
No one was seriously injured.
A spokesman from British Transport Police said: "One police officer was injured and one man was arrested at the scene after a serious disturbance at Glasgow Central Station.
"Around 40-50 youths were involved.
"It is believed to be linked to football fans."