The Manchester United striker played the full 90 minutes of Saturday's 3-2 win at Aston Villa, providing the assist for Javier Hernandez's late winner.
But like fellow Red Devils forward Wayne Rooney, the Dutchman has withdrawn from international duty due to injury.
Coach Louis van Gaal has called up Wolfsburg's Bas Dost as a replacement but Van Persie's departure is set to clear the way for Klaas Jan Huntelaar to start the game in Amsterdam.
Huntelaar, who plays in Germany for Schalke, will feel the opportunity is deserved having scored 34 goals in 59 matches for his country compared to Van Persie's record of 31 in 71 games.
Holland will be seeking revenge against their long-time rivals given that they were beaten 2-1 by Germany at Euro 2012 and thrashed 3-0 in a friendly between the teams in November of last year.