The assault happened around 2.50pm on Sunday, September 30, during a match between Livingston and Rangers.
An assistant referee was struck by an object, thought to be a coin, which was thrown from the stand.
The assistant referee sustained a minor injury to the back of his head and was treated at the scene.
Police were in attendance and officers are now appealing for witnesses to come forward.
Superintendent Craig Smith, Event Commander for the match, said: “This is a shocking incident and it is not the type of behaviour we have come to expect from football fans in Scotland.
“We will not tolerate offences of this nature. With this in mind we are eager to trace the person who was spotted throwing an object from the stand.
“I would also ask anyone who has information that can assist our inquiries to get in touch with us immediately. I would also ask anyone who has any photos or footage of this incident to submit this to police.”
Those with information can contact officers at Livingston Police Station on 101, quoting incident number 1324 of September 30, or anonymously via Crimestoppers on 0800 555 111.