The player is ruled out for South Africa's upcoming test matches.
Springbok prop Wessels has received a ban of nine games for making contact with opponent Josh Murphy's private parts during the Bulls' United Rugby Championship victory over Connacht.
The altercation took place in the early stages of the Bulls' 28-27 win in Galway on Friday, with opposing player Josh Murphy being shown a 20-minute red card after responding aggressively by hitting Wessels on the head.
After Murphy reported the incident to the match official, the event was checked by the TMO, who determined no conclusive video evidence.
Wessels remained on the field until he was substituted in the later stages of the game.
Although the URC announced that the Irish player's temporary sending-off was overturned by a disciplinary panel, Wessels was deemed to have violated the code of conduct, which specifies:
"A player must not engage in actions that is against the principles of fair play. This includes touching, twisting or compressing the private areas."
Disciplinary officials concluded that the incident met the red card threshold and warranted a 12-week suspension, the minimum suspension under international rugby regulations for such an offence.
However, Wessels' suspension was reduced by 21 days 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 ban will rule the 24-year-old out of the South African national team's fall internationals against the Brave Blossoms, France, the Azzurri and Ireland.
Wessels will additionally be absent for the his club's URC games against Glasgow, the Lions and the Sharks, as well as Investec Champions Cup games with Bègles and Northampton.
Wessels has earned 10 caps for the Springboks and was included in their Rugby Championship-winning squad over the summer.
The Connacht player, meanwhile, is eligible to play against the Irish rivals in Saturday's inter-provincial derby after being exonerated.
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