The incident happened during the Raith Rovers v Dundee United game at Stark’s Park in Kirkcaldy, Fife on March 18 this year.
Rovers player Ross Matthews was hit by the coin, which was thrown from the away end of the ground, but was not injured.
Police launched an investigation and have now issued a CCTV image of a man they want to trace.
He is white and in his early to mid 20s, with a heavy build, dark hair and stubble. He was wearing dark clothing during the match.
Constable Jez Graves said: “Reckless behaviour like this could have resulted in serious injury and such behaviour cannot be tolerated.
“Anyone who recognises the man pictured in the CCTV image, or who has any other information relevant to our ongoing inquiries, is asked to get in touch immediately.”