He was sent to the stands by referee Jon Moss, but stood in the tunnel entrance and refused to move as he tried to watch the remainder of the game.
Taylor appeared to encourage Wenger to move away, but the Frenchman was seen pushing back against him.
Arsenal snatched a winner at the death when they were awarded a penalty of their own, which was converted by Alexis Sanchez.
Arsenal travel to face Southampton in the fourth round of the FA Cup on Saturday, before they host Watford in the Premier League three days later.
The other matches Wenger will miss are league encounters away to Chelsea on Feb. 4 and at home to Hull City a week later.
He will return to the dugout should Arsenal reach the FA Cup fifth round or for their Premier League trip to Liverpool on March 4.