The Dutchman suffered the injury after scoring a hat-trick in Wednesday's 3-0 UEFA Champions League win over Olympiacos, a result that saw United through to the last eight where they will meet Bayern Munich.
However, the setback means that Van Persie will miss the visit to Upton Park, and Moyes is not clear as to the extent of the problem.
"We're getting Robin re-scanned today (Friday)," he said. "We're not quite conclusive on everything we've seen.
"We want to just check that out and be sure. He won't be available for tomorrow's game, but we'll try to give you some update when we can on the outcome of it."
United travel to a West Ham outfit who have won the past three home matches, and Moyes is well aware of the threat posed by Sam Allardyce's men.
"I think Big Sam has just won manager of the month," he said.
"I don't know if that was his curse last week or if it's still to come this week. But he's done great.
"They were at a lower league position and he's turned them around.
"We've got a lot of games coming up, we need to make sure that the squad's ready for all the games.
"That's big for us, that we have all our players fit and available."
