The champions were held to a 1-1 draw at Stoke with Nani's strike cancelled out by Peter Crouch.
It meant United's 100% start to the Premier League season came to an end in Rooney's absence and the 25-year-old had earlier 'Tweeted' that he was "gutted" he had been unable to play, but hoped he would be fit to feature in the Champions League clash with Basle at Old Trafford on Tuesday.
However, when asked about Rooney's condition after the match at the Britannia Stadium, Ferguson told MUTV: "It is difficult to say. It's a hamstring. It is not a serious one, it is a mild one.
"I don't think he will be available for next week. It will be more than a week out."