The player is ruled out for South Africa's fall fixtures.
South Africa front-rower Wessels has been suspended of nine games for touching opponent Josh Murphy's genitals during the Bulls' United Rugby Championship win over the Irish province.
This event happened in the early stages of the Bulls' 28-27 win in Galway on last Friday, with Connacht forward Murphy being shown a 20-minute red card after reacting angrily by striking Wessels on the head area.
Following the Connacht player complained to the match official, the situation was examined by the television match official, who determined insufficient clear footage.
The Bulls player remained on the field until he was substituted in the later stages of the game.
While the United Rugby Championship confirmed that Murphy's temporary sending-off was overturned by a governing body, the Springbok was deemed to have breached the code of conduct, which declares:
"Any athlete must not do anything that is against the spirit of good sportsmanship. This includes touching, pulling or squeezing the private areas."
The panel determined that the event reached the level for dismissal and justified a three-month ban, the shortest ban under World Rugby rules for such an violation.
However, Wessels' ban was shortened by three weeks because of his cooperative behavior during the proceedings and his good record.
Wessels and the Pretoria-based team have the right to appeal, but as it stands, the suspension will prevent the 24-year-old out of the South African national team's fall internationals against Japan, Les Bleus, Italy and Ireland.
He will also miss the his club's league matches against Warriors, the Emirates Lions and the Sharks, as well as European cup games with Bordeaux and Saints.
The prop has won 10 caps for South Africa and was part of their Rugby Championship-winning squad during the recent tournament.
Murphy, meanwhile, is available to play against the Irish rivals in this weekend's domestic clash after being cleared.