Ferguson also said that the midfielder will have a plate inserted into his arm but he will still be able to train.
Giggs has been one of United's most consistent performers this season and his absence will be a loss for Ferguson and his men as they chase a Carling Cup, Champions League and Premier League treble.
His injury comes at a particularly bad time for United as winger Nani must serve a three-match ban, which will incorporate the Carling Cup final, following his dismissal at Villa Park.
Giggs, the most decorated player in English football with 11 Premier League winners' medals, does not feature for United in every game, but he has made 22 appearances for United so far this season, scoring four goals.
The veteran midfielder has gained recognition for his fine form and longevity by winning a number of accolades in the past 12 months, including the 2009 BBC Sports Personality of the Year and the Professional Footballers' Association Player of the Year award back in April.
Giggs's injury cast a cloud over what was an otherwise satisfactory evening for United at Villa Park as they moved to within a point of Premier League leaders Chelsea, who suffered a 2-1 defeat at Everton.
It was, in the end, a well-earned draw, especially considering United were reduced to 10-men after Nani was shown a straight red card for a 28th-minute lunge on Stiliyan Petrov.
Although Ferguson will lament the loss of Giggs, he will have defender Rio Ferdinand back for next week's Champions League tie at the San Siro while centre-back Nemanja Vidic was nearing full fitness following a nerve problem.
United have almost an entire week to prepare for the trip to Italy following their surprise FA Cup third-round defeat by Leeds last month.
"In terms of preparing for a European tie we are pleased to have a free weekend," said Ferguson.
"AC Milan are playing on Friday night. That is the kind of help European teams get from their countries. We don't get that here.
"By fortune we don't have a game on Saturday because we are out of the FA Cup and we are going to take full advantage of it."
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