The match finished in a 1-1 draw, thanks to a first-half penalty from Dons striker Sam Cosgrove and a second-half equaliser from Light Blues defender Joe Worrall.
But there were clashes between the two sets of supporters, and police have already launched a probe after a video emerged showing a seat being thrown from the Rangers fans into a section of home supporters.
A spokesperson for the police confirmed they were also looking into reports of seats being thrown “by both home and away supporters towards opposing fans”.
Aberdeen have claimed a total of 60 seats were broken beyond repair in the away end and will have to be replaced at a cost of £45 each.
Six people were arrested during the match for “disorder related” offences and the use of a pyrotechnic device, police said.
Superintendent Richard Craig, the match commander, said: “I would like to thank the vast majority of supporters from both clubs who heeded our advice and behaved responsibly.
“However, it is disappointing that a very small minority of fans chose to ignore the warnings and were involved in disorderly behaviour.
“They have let themselves and their clubs down. Disruptive behaviour in and around football matches in Scotland will not be tolerated and those who choose to conduct themselves in such a way will be firmly dealt with.”
A report will be prepared and sent to the procurator fiscal in relation to the offences.