The Canaries lodged an appeal to the Football Association after Johnson was sent off following an altercation with Newcastle striker Loic Remy, who was also dismissed.
Johnson will now be available for Norwich's Premier League game at Cardiff City on Saturday.
Norwich boss Chris Hughton told the club's official website: "It's very good news for us. Our feeling at the time was that it was a very harsh decision so credit to those who had to make the decision to uphold our appeal."
Meanwhile, Remy's three-match ban has been upheld following an appeal.