Wenger had been banned for the first leg for comments made about the referee following last season's Champions League elimination by Barcelona.
However, he was seen passing on instructions to the bench through coach Boro Primorac, who sat alongside the manager in the stands.
UEFA ruled that was a breach of its rules, banning Wenger from Wednesday's second leg against Udinese and his next European match. Arsenal was also fined $14,400 for "improper conduct by its officials."
Arsenal said on its website that it would be appealing Wenger's suspension and the club fine.
Arsenal won the first leg 1-0.