Van Persie was carried off on a stretcher in the dying minutes of United's 3-0 win over Olympiacos with a knee injury.
United are unsure how long Van Persie will be out for, but the striker will definitely miss Saturday evening's game at Upton Park.
"We are getting him re-scanned again on Friday because there was nothing conclusive." the United boss said.
"He won't be available for Saturday's game.
"We will give you an update as soon as we can."
United beat Olympiacos 3-0 at home in the second leg of their tie to make it through to the quarter-finals of the Champions League.
They were given the daunting task of facing Bayern Munich in the last eight at Friday's draw in Nyon.
Moyes concedes he has a tough task on his hands.
"I have probably drawn out the favourites," the Scot said.
"They are the holders so it is a really tough draw for us but it's one I am looking forward to."
Unlike the last 16 clash versus Olympiacos, United will play their first leg at home.
The Red Devils, who drifted from 18-1 to 33-1 following the draw, will take on Pep Guardiola's side at Old Trafford on April 1 before they travel to Germany for the return leg eight days later.
"I would prefer to be at home in the second leg," Moyes said.
"But we have got it. That is the way the draw has come out - we just have to take it."
The win over Olympiacos was a welcome relief for Moyes following a difficult fortnight in which his ability to manage the side was brought into question seriously for the first time.
The Red Devils wilted in Athens to hand Olympiacos a two-goal first-leg lead, and then last Sunday United were humbled 3-0 at home by Liverpool in the Barclays Premier League.
That defeat put United on course for their worst ever points total in Premier League.
Moyes was naturally delighted, therefore, to have lifted his spirits and those of the fans in midweek.
"I think the big thing was I could look at the supporters in the face after the game on Wednesday night because I thought we had given them something to shout about, we had nothing to be ashamed of with our performance," the Scot said.
"In some other games I have felt ashamed because the team haven't played well enough and I've not got a team out which has got a good result.
"Our form hasn't been consistent enough, our performances haven't been consistent enough.
"We've obviously got to get better at that. It's going to take time, we're not going to be able to do everything immediately."