The Dutchman missed Sunday's 4-1 defeat to Manchester City with the same injury and Moyes has taken the decision not to risk him in the game with the Reds.
The Scot was also downbeat on Van Persie's chances of being fit for this weekend's clash with West Brom, claiming he faces a race against time to recover for the visit of the Baggies.
"I don't think Robin van Persie will play on Wednesday, but he has an outside chance for Saturday," Moyes told reporters.
Despite the opposition for the third round, Moyes has said he will make changes for the game, with Javier Hernandez, Jonny Evans, Shinji Kagawa, Wilfried Zaha and Anders Lindegaard all expected to start.
Phil Jones and Rafael are unlikely to be included in the squad as they recover from their respective injuries, while Darren Fletcher is a long-term absentee.