The Portugal star suffered the problem during Wednesday's Champions League encounter with Braga. He will miss Saturday's trip to Aston Villa.
Nani is also a major doubt for next weekend's trip to Norwich and could be struggling for the Champions League tie away at Galatasaray on November 20.
"Nani is out with a tight hamstring and that will be around 10 days but he should be okay," said Sir Alex Ferguson. "It's not torn, just tight."
Defender Jonny Evans also suffered a minor groin strain against Braga but could be fit for the trip to Villa Park. Chris Smalling, who made his first appearance since May in the Champions League victory, will fill in if required.
"We're hoping Evans will be okay for Saturday," Ferguson said. "He's a doubt, although not a serious one.
"We're monitoring the situation with Jonny. If he doesn't make it then Chris will have to play.
"It's asking a lot for him to play Wednesday and then Saturday [when he's just come back]. The great thing is that he's back and there are no issues with him at all. He did very well on Wednesday - we were pleased with that."