Police are making enquiries into "pyrotechnics being used and items being thrown" during Dundee United v Aberdeen on Sunday.
United won Sunday's Scottish Premiership game at Tannadice.
A Police Scotland spokesperson said: "We are aware of pyrotechnics being used and items being thrown during the match at Tannadice on Sunday, 29 December, 2024.
"Enquiries into the matter are ongoing."
League organisers the SPFL said: "Players, staff and fellow supporters should, of course, have the right to attend games free from the risk of being struck by projectiles. The dangers involved are obvious.
"Anyone found guilty of such utterly irresponsible behaviour should face criminal charges, as well as being banned from future SPFL games.
"We look forward to receiving the match delegate report and to see what action Police Scotland take in identifying and charging those responsible."
Dundee United manager Jim Goodwin had said after his side's win, which came courtesy of a late Kevin Holt goal: "I tried to be as reserved as I possibly could be when the goal went in.
"It's disappointing again, the amount of missiles that are coming down from above. There was a bottle of vodka, coins, firelighters and everything coming down on us.
"I hope the authorities look at it. Stuff was skimming over our heads and not just mine, my backroom team, the linesmen and the fourth official.
"There was a considerable amount of objects thrown in our direction.
"It's madness in this day and age and hopefully there's plenty of cameras there at the game today, CCTV and all of that.
"Hopefully these guys will be caught and thrown out of football for life."
Dundee United visit near neighbours Dundee on Thursday (17:30 GMT).
And United said in a statement: "Recent high-profile fixtures across Scottish football have highlighted the negative aspects of crowd behaviour and illegal conduct and this is our chance to demonstrate the true spirit of the Dundee derby and positively showcase Scottish football.
"We encourage all supporters to enjoy the occasion with respect and keep all celebrations within the stands.
"We kindly remind everyone attending the match that the use of pyrotechnics is prohibited at the Scot Foam Stadium and all Scottish football grounds. Carrying or using pyrotechnics is not only illegal but also endangers the safety and enjoyment of fellow fans. Please refrain from pyrotechnic use and help each other enjoy the event together."