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's Regulatory Commission told the FA's 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."
Ferguson 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," Ferguson said.
"We have some who are fit. He wasn't fit. He was taking 30 seconds to book a player. He needed 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 he would not be facing action from them over those comments.
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