The Swedish Football Association's disciplinary committee announced the decision on Wednesday and wrote that "what happened should be punished with a suspension."
Gustafson was remorseful after the incident.
Terribly stupid of me, but at the same time it was a quick and smart move by Vasic. I tugged on his hair a little and he pulled off the tassel and ran to the referee. I'm worried about it," he told Fotbollskanalen after the final.
The suspension means that Gustafson will miss the matches against Elfsborg on Thursday and IFK Gothenburg on May 25.
Reigning champions Mjällby are sixth in the Allsvenskan and won the cup final.
