The 26-year-old Wilson, capped 15 times by his country, pleaded not guilty after the incident at a scrum during Sunday's game.
"As the judicial officer was not satisfied to the required standard that the act of foul play as alleged had been committed, the citing complaint was dismissed and Wilson is therefore free to play," European Professional Club Rugby (EPCR) said in a statement.
Wilson, left out of Scotland's Six Nations squad this week, could have faced a minimum 12-week suspension if found guilty of the offence but is now clear to play for his club.
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(Reporting by Ed Osmond; Editing by John O'Brien)
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