However, Graham Kelly, the FA's chief executive, has warned both players that any further conflict would lead to a heavy penalty.
Wright, the Arsenal striker, and the Manchester United keeper, Schmeichel, have been involved in incidents twice this season following challenges by the England international on the Dane.
Schmeichel was alleged to have made racist remarks to Wright during United's 1-0 premiership win at Old Trafford in November. Wright did not hide his anger and the controversy broke out again after an incident during United's 2-1 win at Highbury on 19 February.
The Arsenal striker appeared to go in studs-first with a challenge that drew the United manager, Alex Ferguson, off the bench to make his feelings clear. At the final whistle more words were exchanged as the pair went up the Highbury tunnel with stewards intervening to keep them apart.
The FA decided to step in to what appeared to be an escalating conflict and its director of public affairs, David Davies, yesterday issued Lancaster Gate's official verdict.
Davies said that Kelly had made it clear that disciplinary action would not be in the best interests of the game. Wright and Schmeichel had made it clear that there is no feud and that they have professional respect for each other, although both have been warned of their responsibilities as role models.
Davies' statement read: "Over several weeks the Football Association has been involved in confidential discussions with representatives of Arsenal and Manchester United. These followed incidents involving Ian Wright and Peter Schmeichel. Also involved have been Peter Leaver of the Premier League and Gordon Taylor of the Professional Footballers' Association.
"Ian Wright and Peter Schmeichel and their clubs have assured the FA there is no feud between them and both players have made it clear they respect each other as professionals. Graham Kelly has received expressions of regret from both sides and a recognition of the wider interests of the game.
"Ian Wright has been deeply upset that what he insists were genuine attempts to win the ball have been misinterpreted in some quarters. It has already been said publicly by Manchester United on Peter Schmeichel's behalf that he is not a racist and never will be."
Kelly has written to Schmeichel, Wright and to their clubs, leaving the players in no doubt of their responsibilities when they next meet on the pitch. Failure to meet these standards "will be very serious".
The FA has opened an investigation into a mass brawl that disfigured a match between the youth teams of the ground-sharers, Crystal Palace and Wimbledon. A racist remark is alleged to have sparked the trouble and now the clubs been asked for their observations.