Wenger, 67, pushed Taylor after being sent off in the closing stages of the Gunners' 2-1 win at Emirates Stadium.
He had been dismissed for reacting angrily to a 93rd-minute penalty given to Burnley, who trailed 1-0.
An FA statement read: "It is alleged that in or around the 92nd minute, 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."
Wenger, who later apologised, has until 18:00 GMT on Thursday to respond.