Van Persie played the full 90 minutes of United's 3-2 victory over Aston Villa on Saturday but has now dropped out of Louis van Gaal's party for the midweek game.
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Wolfsburg striker Bas Dost will replace Van Persie in the squad for the fixture. Van Gaal has been forced to leave four other players out of his plans for the match in Amsterdam.
The encounter will come too soon for goalkeeper Maarten Stekelenburg, midfielder Kevin Strootman and attackers Luciano Narsingh and Jermain Lens, so RKC goalkeeper Jeroen Zoet and Feyenoord trio Jordy Clasie, Ruben Schaken and Stefan de Vrij have been called up.
Although Dost has been summoned to replace Van Persie, the prolific forward's injury is likely to open the way for Klaas-Jan Huntelaar to start at centre forward.
The Schalke star has scored 34 goals in his 59 appearances for his country, which compares favourably to Van Persie's record of 31 goals in 71 international matches.
Manchester United are back in action on Saturday when they play Norwich City in the Premier League at Carrow Road.