The Dutchman picked up a calf injury in the Netherlands' 2-0 win over Turkey on Tuesday and may not line up against the Saints at Old Trafford, while Antonio Valencia and Javier Hernandez are also doubtful.
"Probably the one we're most worried about is Robin van Persie," Moyes told MUTV.
"Antonio is very late coming back from South America, Chicharito too. They're the ones who always have long-haul flights, but we're a bit worried about Robin and the condition he's come back in."
"It's an incredible achievement and I've spoken to him about it," the 50-year-old added.
"I think what he wants to do now is go on and score more goals for Holland and do it in the World Cup where it matters.
"There have been some brilliant Dutch centre-forwards over the years - to be at the top of that list is something special for him."
Van Persie has scored four goals in eight appearances for United this season.