Fans of the Dutch giants reportedly tried to break through a security cordon at the ground, ripped up seats and hurled them at stewards.
As reported in yesterday's Evening Times, trouble flared in the Ajax section of the ground after James Forrest scored from the penalty spot to put Celtic 1-0 up.
Tensions intensified after final whistle blew, leaving the Amsterdam side 2-1 losers to 10-man Celtic.
Ajax now face disciplinary action from Uefa, after a case was opened against them, following Tuesday night's disorder.
Uefa has accused the Dutch club of being responsible for "crowd disturbances and throwing of objects" during the match, a contravention of Uefa Disciplinary Regulation 16.
Their case will be heard by the Uefa Control and Disciplinary Body on Thursday November 21.
Police Scotland confirmed no Ajax fans were arrested during Tuesday night's game at Parkhead.
However, an investigation into the behaviour of some fans is now underway.
A Police Scotland spokeswoman, said: "Our officers are reviewing CCTV images.
"Any information gleaned will be shared with our Dutch counterparts."
Before kick-off, officers were out in force in Glasgow as streets and pubs were flooded with 3000 visiting fans.
There was a heavy police presence in Sauchiehall Street to Trongate and Gallowgate.
Meanwhile, members of the public flagged up trouble and posted pictures online showing hundreds of chanting Ajax fans being led through the city by officers.