The bottle landed in the home section of the South Stand of Pittodrie Stadium shortly before the end of the SPFL match between Aberdeen and Rangers on Sunday, 5 August.
It was reported a 12-year-old boy was hit by the bottle in a “glancing blow”, but was not injured.
Officers have released images of a man they want to trace, who is understood to have been in the South Stand away section during the game, which ended in a 1-1 draw.
Police Constable Connor McKeen, from the Divisional Alcohol Violence Reduction Unit (DAVRU), said: “Whilst no-one was injured, this reckless behaviour could have resulted in serious injury.
“Police Scotland is committed to ensuring spectators at football matches are kept safe and that the individuals responsible for anti-social behaviour are held to account.
“I would appeal to anyone who recognises the man pictured or has any knowledge of this incident to come forward and contact the police.”
Anyone with information is asked to contact Police Scotland on 101 or Crimestoppers on 0800 555 111.