The incident happened late in the Europa League match at the PSV Stadium in Eindhoven and goalkeeper Marko Dmitrovic carried on playing, apparently unhurt.
After being hit, Dmitrovic subdued the fan, who was quickly surrounded by players from both teams and then led away as many supporters in the stadium booed.
The Serbian goalkeeper was a late inclusion in Sevilla's starting lineup after Yassine Bounou felt ill before the match.
"I never saw anything like it," Dmitrovic said when he was asked about the incident after the game. "I'm not going to say what I really wanted to do [to the pitch invader]. I'm glad I was aware of where he was coming from and was able to stop him, otherwise other things could have happened. He wanted to hit me, it's unfortunate that this kind of incident happened on a soccer pitch. UEFA should do something, this has to stop."
"It's a disgrace that the game resumed," Sevilla coach Jorge Sampaoli said after the match.
"These acts have to be strongly punished. Otherwise it will happen again and we will not know when it is time to stop when faced with these types of situations."
He added: "I truly don't understand how the referee did not take another decision. If you accept this, from now on, anything could happen."