The player will miss for South Africa's autumn internationals.
Springbok front-rower Wessels faces a suspension of nine matches for grabbing Josh Murphy's private parts during the Bulls' United Rugby Championship win over Connacht.
The altercation occurred in the 18th minute of the Bulls' 28-27 win in Galway on Friday, with opposing player Murphy receiving a temporary dismissal after striking back by hitting the South African on the head area.
After the Connacht player reported the incident to the match official, the event was examined by the TMO, who concluded no conclusive video evidence.
The Bulls player remained on the pitch until he was replaced in the second half of the game.
Although the United Rugby Championship confirmed that the Irish player's 20-minute red card was withdrawn by a disciplinary panel, Wessels was found to have violated the code of conduct, which states:
"A player must not engage in actions that is contrary to the spirit of good sportsmanship. Such behavior covers touching, pulling or compressing the private areas."
Disciplinary officials determined that the contact reached the red card threshold and warranted a 12-week suspension, the minimum suspension under international rugby regulations for such an infringement.
Nonetheless, Wessels' ban was shortened by 21 days because of his good conduct during the proceedings and his clean disciplinary history.
The forward and the Bulls are entitled to appeal, but currently, the suspension will rule the 24-year-old out of the Springboks' fall internationals against the Brave Blossoms, Les Bleus, Italy and Ireland.
Wessels will also miss the Bulls' URC games against Glasgow, the Lions and the Cell C Sharks, as well as Investec Champions Cup fixtures with Bordeaux and Saints.
The prop has won 10 caps for South Africa and was included in their Rugby Championship-winning team during the recent tournament.
The Connacht player, in contrast, is available to play against Munster in this weekend's inter-provincial derby after being cleared.
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