The 30-year-old was carried off on a stretcher near the end of United's Champions League victory over Olympiacos on Wednesday evening, and after a scan failed to reveal the extent of the damage, manager David Moyes has revealed that the Dutchman will sit out the trip to Upton Park.
The Scot told reporters: "We are getting him re-scanned again on Friday because there was nothing conclusive.
"He won't be available for Saturday's game. We will give you an update as soon as we can."
Van Persie, who netted a hat-trick on Wednesday evening, has scored 17 times in 25 appearances for United during the current campaign.