The Portuguese has been an unused substitute in two of United's last three matches, including Wednesday's Capital One Cup quarter-final win at Stoke City, and will now not play until the turn of the year.
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"Nani has got a hamstring injury and we were worried about that. It's worse than we hoped so that might well keep him out for a few weeks," Moyes told reporters.
"The players have done really well. That is why there is such a good squad and a big squad here because throughout the season, the amount of games we have to play here, you do need those extra players.
"We have seen recently, in the last couple of games, we have been a little bit short in areas but the players who have come in have done brilliantly well. We have needed the whole squad, we really have.
"Bringing Darren Fletcher back into it as well [following his lengthy layoff with a bowel condition] has given everybody a lift."
United's victory over Stoke represented the reigning league champions' third in succession following back-to-back defeats at home to Everton and Newcastle United.
"We've had three wins and three clean sheets from the past three games - I'm really pleased," Moyes said.
"We are getting into our stride and that's exactly what I want. Putting runs together is normal at Manchester United."