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."
In the absence of Rooney, Ashley Young took on scoring responsibilities at Stoke on Wednesday, with Danny Welbeck netting twice at Aston Villa last weekend.
It has been part of a three-match winning streak for only the second time this season, with Moyes keen for that run to be extended.
"We have had three really good wins and three clean sheets as well, so I am really pleased," said the Scot.
"The players have played well and I am really happy with how they have done in recent weeks.
"It is more to do with getting into their stride and hopefully this is the way it goes in the future.
"This is what we want. We are trying to get back to as much normality as we possibly can."