The FA handed down the punishment on Monday after Wenger was charged for pushing fourth official Anthony Taylor after he was sent to the stands for protesting a penalty decision in Sunday’s win over Burnley.
He was also fined £25,000 for his actions, and will have to spend the next four games sitting in the stands.
Wenger was also charged with using insulting language toward the officials. The Arsenal boss has apologised for his actions and accepted the charge.
“It was alleged that in or around the 92nd minute, he used abusive and/or insulting words towards the fourth official,” an FA statement said.
“It was further alleged that following his dismissal from the technical area, his behaviour in remaining in the tunnel area and making physical contact with the fourth official amounted to improper conduct.”