Defender Vidic trained ahead of the team's departure on Tuesday but did not travel due to a concussion, while striker Van Persie has stayed at home because of a groin problem.
"They are both injured," said Moyes. "Neither of them are long-term but they are not quite ready yet."
However, versatile England international Phil Jones has made the trip to Germany, having recovered from the groin injury which sidelined him for Sunday's 2-2 draw at Cardiff.
But Moyes is still a little short of numbers in midfield because Michael Carrick has an Achilles injury and Marouane Fellaini is suspended following his red card against Real Sociedad.
Moyes said: "It is normal to lose players to injury and suspension at big clubs but we have a squad which we will be able to use and they can show what they
United know that a win against Leverkusen will seal their place in the last 16 of the competition, although a draw could also be enough should Shakhtar Donetsk lose to Sociedad in the other game in Group A.
Bayer have only failed to win one match at home this season - against Champions League holders Bayern Munich - and Moyes added: "We'll have a game on our hands.
"We have to make sure we're defensively sound and also that we go out there to win the game.
"We had a great opportunity in Sociedad to pull away further but we didn't
"We want to try and get the work done as soon as we possibly can but, if it has to go to the last game, so be it."
Bayer Leverkusen v Man United is live on Sky Sports 2 on Wednesday, kick-off 7.45pm