Van Persie picked up a calf problem against Turkey on Tuesday night and Moyes feels he may struggle to feature against Saints at Old Trafford on Saturday.
United trail Mauricio Pochettino’s team by four points after a problematic start to Moyes' reign and Van Persie is yet to hit the heights that saw him top the goalscoring charts in last season’s Premier League.
Discussing the club’s injury problems, Moyes told MUTV: "We have a few with knocks.
"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."
However, the Scot did reveal that Fellaini, who is playing with a protective cast on his arm, should be fit for the foreseeable future as United look to delay an operation.
"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."
Moyes also praised Van Persie for overtaking Patrick Kluivert’s all-time Netherlands goalscoring record following his hat-trick against Hungay.
"It is an incredible achievement," Moyes added.
"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."