United boss David Moyes confirmed the Holland international had suffered the injury when he took the corner that led to Phil Jones' match-winner in the Champions League triumph over Shakhtar Donetsk on Tuesday.
"Robin van Persie is out for a month," said Moyes.
"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."
With Nemanja Vidic, Patrice Evra and Chris Smalling also sidelined for the Shakhtar game, and his side suffering back-to-back Premier League defeats against Everton and Newcastle, it must feel as though Moyes is having no luck at present.
However, he said: "I have no doubt it will get better.
"I am sure we have plenty of players who can cover it and we don't miss them too much."
At least Moyes does have alternatives to Van Persie. In midfield his squad has been left bereft by the absence of Michael Carrick, who has been sidelined for a month with an Achilles injury.
As Moyes had already identified central midfield as a problem area when he took over last July, it has merely exacerbated a situation that Press Association Sport understands will become priority number one during next month's transfer window.
"I do (feel United have felt Carrick's loss)," said Moyes
"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.
"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."