The Frenchman was sent to the stands in injury time of the 2-1 victory after clashing with Taylor, towards whom he was also charged with using abusive or insulting language.
Wenger was also penalised for remaining in the tunnel area to watch the final minutes of the match.
As a result, he will not be in his technical area for the Gunners' crucial Premier League fixture against Chelsea on February 4 as well as three other games.
The incident in question occured after he was sent off after complaining to referee Jon Moss about the awarding of a 93rd-minute penalty to Burnley, which Andre Gray converted to equalise before Alexis Sanchez netted a spot-kick of his own to seal a dramatic win for Arsenal.
After moving to stand in the tunnel amid a heated exchange with fourth official Taylor, Wenger appeared to push the official as he attempted to usher him away.
The 67-year-old apologised for his actions and requested a personal hearing with the Football Association, which took place on Friday before his suspension was announced.
"I regret everything," Wenger said after the game. "I should have shut up and gone home basically. And I apologise for that.
"It was nothing bad, I said something that you hear every day in football. Overall nine times out of 10 you are not sent to the stands for that but if I am I am and I should have shut up completely.
"I was quite calm the whole game, more than usual, but just in the last two or three minutes…"
A statement from the FA reads: "Arsene Wenger has been given a four-match touchline ban with immediate effect after he was charged for misconduct following Arsenal’s game against Burnley on Sunday 22 January 2017.
"It was alleged that in or around the 92nd minute, he used abusive and/or insulting words towards the fourth official.
"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.
"The Arsenal manager, who was also fined £25,000, admitted the charge and requested a personal hearing which took place before an Independent Regulatory Commission [on Friday]."