Sturm Graz issued an apology after the assistant referee sustained a cut to the head in their Europa League tie against AEK Larnaca and said the person responsible has been caught.
Fredrik Klyver appeared to be struck by a cup thrown from the crowd during Thursday's tie at Merkur Arena, leading to a long delay as he received treatment.
The teams were taken off the field by referee Mohammed Al-Hakim and, when they emerged, Klyver had been replaced by the fourth official.
"This behaviour of a fan in today's Europa League game is by no means acceptable," said a Sturm Graz statement released after the match.
"This damages the reputation of football and us as a club. We always try to see football as a positive celebration and to tackle these exact things.
"Fair play is our top priority. We are sorry that today we have disappointed many football fans.
"The cup thrower was caught. The possible punishments will be considered.
"Sturm Graz wishes the linesman all the best and speedy recovery."
The Austrian side lost the game 2-0 to goals from Joan Truyols and Ivan Trickovski, while they had Stefan Hierlander sent off in the 94th minute.