The Dutchman recently returned from a four-game lay-off due to a groin problem, playing in last weekend's 1-0 loss to Newcastle United and the midweek victory over Shakhtar Donetsk in the UEFA Champions League.
However, he injured himself as he took the corner that led to Phil Jones's 67th-minute winner against Shakhtar and Moyes expects him to be out of action until next year.
"Robin Van Persie is out for a month," Moyes said. "He picked up a thigh strain in taking a corner kick which led to the goal."
Moyes added: "It is unfortunate because I think if you look at our record with Wayne Rooney and Robin in the team, it is actually very good and we have not had them for quite a period recently.
"Marouane Fellaini has a bit of a back injury. Michael Carrick is missing and Robin is going to miss four weeks with a thigh strain. That is a big blow to us."
United's top scorer last season, Van Persie has scored seven goals in 11 league appearances this term.
News of his injury comes as United bid to bounce back from successive home defeats in the league, which have left them 13 points behind leaders Arsenal.
However, while Moyes has several alternatives in the forward positions -- notably Javier Hernandez and Danny Welbeck -- Carrick's absence with an Achilles problem leaves him bereft of options in central midfield.
Asked if he felt that Carrick's lay-off had hurt United, Moyes replied: "I do. We need him for his creativity. We have missed him for lots of other reasons as well. It is important.
"We were looking for a couple of midfield players in the summer. We weren't able to get two. We got one (Fellaini).
"We needed one who could give us something else if we did get an injury to Michael or one who could have played with him. We have definitely been a little bit short in that area.
"Hopefully he is not too far away and he will be back in a couple of weeks."
Moyes, whose side visit Aston Villa on Sunday, also moved to quash suggestions that his predecessor Alex Ferguson remains a big influence at the club.
Former United captain Roy Keane said on British television this week that he believes the former manager, who is now a director at Old Trafford, wants to control the club and still wields a lot of power.
But Moyes refuted those suggestions, insisting that he is the one who gets in touch with Ferguson, rather than the other way round.
"I can only tell you that in my time here Alex has been fantastic and helpful," he said. "Anytime I need something, I can go to him. He's been very good."
No team has ever come from 13 points back at this stage of the season to win the Premier League, but Moyes wants the players to use it as a source of motivation as they seek to close the gap on leaders Arsenal and the other teams who sit above them.
"We do see it as a challenge," he said. "We have a long way to go. We can only take one game at a time and let's see what happens later on in the season. We can't talk about it now. We will do when we are closer."