At a personal hearing in London, Ferguson, 67, admitted a charge of improper conduct for questioning Wiley's suitability to officiate following United's 2-2 draw with Sunderland at Old Trafford on October 3.
Ferguson said Wiley was not fit enough to referee the game.
Peter Griffiths, the chairman of the FA Regulatory Commission, told the FA website: "Each member of the Commission recognised Sir Alex Ferguson's achievements and stature within the game.
"Having said that, it was made clear to Sir Alex that with such stature comes increased responsibilities.
"The Commission considered his admitted remarks, in the context in which they were made, were not just improper but were grossly improper and wholly inappropriate. He should never have said what he did say."
Alan Leighton, head of the referees' union Prospect, said Ferguson had got off lightly.
"From our point of view, it is disappointing," he told the BBC. "The Football Association had a chance to make a point and they flunked it.
"We don't think this is sending the right message out to other managers... if he is seen to be getting off lightly, other managers may think what he said was not beyond the pale."
Ferguson had criticised Wiley in a television interview, saying: "He was not fit enough for a game of that standard."
"The pace of the game demanded a referee who was fit. It is an indictment of our game. You see referees abroad who are as fit as butcher's dogs.
"We have some who are fit. He wasn't fit. He was taking 30 seconds to book a player. He was needing a rest. It was ridiculous."
Ferguson also criticised referee Martin Atkinson after Manchester United lost 1-0 at Chelsea in the Premier League on Sunday.
"You lose faith in the refereeing sometimes -- that's the way the players are talking in there," he said after the match.
The FA, however, said on Monday Ferguson would not face action from the governing body over those comments.
