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.”