The Portugal winger has not featured since the home defeat to Newcastle on December 7 and has recently been linked with a move to Juventus.
"Nani has a hamstring injury which is a little bit worse than we thought," said Moyes.
"He is probably going to be missing for a few weeks."
It merely adds to an injury list that already includes Robin van Persie and Michael Carrick.
Wayne Rooney is also a major doubt for Saturday's encounter with West Ham as he tries to overcome a groin strain, although Moyes is not ruling him out just yet.
"He has a chance," said Moyes. "We will see how he is tomorrow."
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