Wenger was sent to the stands in stoppage time of Arsenal’s 2-1 Premier League win at Emirates Stadium, having complained to referee Jon Moss, who awarded the visitors a 93rd-minute penalty, which Andre Gray converted to equalise.
A heated exchange with fourth official Anthony Taylor followed before Wenger moved to stand in the tunnel.
The Frenchman then appeared to push Taylor as the official tried to usher him away, with stewards forced to intervene.
A Football Association statement read: “It is alleged that in or around the 92nd minute, he [Wenger] used abusive and/or insulting words towards the fourth official.
“It is 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.”