The 30-year-old striker - who has scored seven goals in 10 Premier League appearances this season - missed United's 2-2 draw with Cardiff City on Sunday with the problem.
Manager David Moyes had hoped the Netherlands international, on target in a 4-2 victory in the reverse fixture at Old Trafford in September, would recover for the midweek UEFA Champions League game, but Van Persie has not made the journey to Germany, along with defender Nemanja Vidic.
"Robin isn't quite ready yet," Moyes said. "It's not long-term, but we're going to keep monitoring him."
The Premier League champions will also be without Vidic, who is still recovering from concussion sustained in United's 1-0 win over Arsenal on November 10.
Moyes, though, has been handed a defensive boost as Phil Jones trained on Tuesday after overcoming a knock he picked up on international duty with England that forced him to miss the Cardiff game.
Van Persie's absence will be keenly felt as United go in search of a win that will seal progression to the knockout stages from Group A.
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