Van Persie picked up a calf injury on international duty with Holland after reporting for duty with a toe problem.
"We have a few with knocks," Moyes told MUTV.
"The one we are more worried about is Robin van Persie.
"He got a kick on the calf and he came off in the second game (against Turkey). He has had problems with his toes as well.
"We will see how he is."
Van Persie's hat-trick against Hungary last Friday took him top of the Dutch international scoring charts.
"It is an incredible achievement," said Moyes.
"What he wants to do now is score more goals for Holland and do it in a World Cup when it matters.
"But there have been some brilliant Dutch forwards over the years and they have had an array of talent. To be at the top of that list is something special."
Meanwhile, Moyes also confirmed Belgium midfield man Marouane Fellaini could delay an operation on his wrist for up to two years.
Fellaini has been playing with a protective cast on his hand during the recent internationals and, with Tom Cleverley ruled out by a groin injury, the £27.5million man will have to keep going for a good while yet despite the obvious discomfort.
"Fellaini needs an operation," said Moyes.
"It is quite a bad wrist injury. There is a bit of bone and ligament sticking out.
"We have been told we can get away without operating just now and we are a little bit short with Tom Cleverley picking up a calf strain for England, so we need him and we will put it off as long as we can.
"That could be as long as two years.
"It is not desperate but part of it is does he feel OK to play.
"You do use your arms to hold people off and we have to make sure his wrist is not suffering any more damage than it is already."