The Portugal international has not been named in a matchday squad since the League Cup win over Stoke on December 18, having sustained the problem in training.
He will be unavailable for David Moyes for the forseeable future, although the United manager expects defender Rafael to return soon.
"Nani has got a hamstring injury which is probably going to keep him out for quite a while," he told the club's official website.
"It's a serious hamstring injury that he picked up in training.
"I don't think Rafa is too far away, though, as his injury isn't too serious. Hopefully, we're beginning to get one or two back."
Rafael was withdrawn after 18 minutes of United's 3-2 victory against Hull City in the Premier League on December 26.
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