Ferguson claimed the 49-year-old official was unfit after taking charge of his side's 2-2 draw with Sunderland at Old Trafford on Saturday.
Having looked at the remarks, the FA have now requested that the Scot explains the reasons behind his outburst.
However, no further action will be taken against Blackburn manager Sam Allardyce who criticised Peter Walton for not giving Rovers a penalty in their 6-2 defeat at Arsenal.
Ferguson's comments have been criticised by Alan Leighton, national secretary of professionals' union Prospect - who represent referees.
"My main concern is about the unfounded and totally unwarranted remarks about Alan Wiley's fitness," he said.
"Not only does it dig at the heart of Alan's professionalism, where he is one of our top and longest-serving referees, but it also has an impact on all the others.
"Sir Alex made comments about other referees and said about European referees being fit as butchers' dogs, comparing them with some referees from the UK who aren't fit.
"All of the referees, all of the officials and all of the assistant referees pass stringent fitness tests at the start of the season.
"Prozone statistics are used to monitor their performance in every game. If Alan Wiley or any other referee were not fit they would not be refereeing."
Ironically, on his official Premier Game Match Officials Ltd profile, Wiley makes a point of highlighting the importance of keeping up with the physical side of the game.
"Firstly, you have to be fit enough to cope with an ever increasing speed of the game," he said.
After the Sunderland match Ferguson said he thought Wiley was off the pace.
"He was also walking up the pitch for the second goal needing a rest. He was not fit enough for a game of that standard," said the United boss.
"The pace of the game demanded a referee who was fit. He was not fit. It is an indictment of our game.
"You see referees abroad who are as fit as butchers' 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."
Former Premier League referee Dermot Gallagher - a close friend of Wiley - felt Ferguson's comments were out of order.
"In the 17 years the Premier League has been going this is the
first time I have ever heard a manger use that criticism of a referee," Gallagher told Sky Sports News.
"I hear all kinds of things and I have never known a manager to say a referee wasn't fit enough.
"In the year 2009 with the training they have got now, it's the most ridiculous comment I have ever heard.
"The referees are fit for purpose. They are training four, five, six times a week.
"They are training to an intensity which 10 years ago I would never have believed."
Ferguson has frequently courted controversy for his comments about referees over the years.
He was warned about his conduct in 2008 after criticising referee Martin Atkinson for failing to give United a penalty in the FA Cup quarter-final defeat to Portsmouth.
And in 2007 he questioned Phil Dowd's competence after the referee sent off Paul Scholes and Wayne Rooney
in United's 2-0 Premier League defeat at Fulham.
Allardyce escaped censure after questioning the quality of refereeing in the top flight after Walton missed Thomas Vermaelen's apparent trip on David Dunn.
"It was a blatant penalty. There is no doubt in my mind that the position of the referee was excellent," said the Blackburn boss.
"He just didn't, unfortunately, give the decision in our favour. It is human beings in a very big pressure position.
"In the big pressure pot that is this league, you have got to get the major decisions right otherwise you don't stay in this league too long, not as a manager or a player, so as a referee you have got to be judged the same.
"They are fully professional now so if they are not good enough, we should find someone who is."