Both men have been charged with improper conduct for "inappropriate language" directed at the match official in the aftermath of a 3-1 defeat at Camp Nou, according to UEFA. The disciplinary case will be heard on March 17.
Arsenal were infuriated by Busacca's decision to show a second yellow card to striker Robin van Persie in the second half of the Champions League last-16, second-leg tie.
Having already been booked for pushing Barca defender Dani Alves in the face, Van Persie was adjudged to have kicked the ball away in the second half, despite only a second elapsing between the whistle being blown and Van Persie taking a shot at goal.
Van Persie desperately argued that he had not heard the whistle when playing in front of a crowd in excess of 95,000, but Busacca reduced Arsenal to ten men with 56 minutes gone.
After two goals from Lionel Messi and a strike from Xavi condemned Arsenal to an early exit from the competition, Wenger was involved in a heated confrontation with Busacca. Both he and midfielder Nasri have now been charged by European football's governing body.
However, there is no indication that Van Persie himself has been charged, despite calling Busacca a "joke" in a post-match interview.