The 30-year-old was taken off with five minutes remaining as United defeated Premier League leaders Arsenal 1-0 at Old Trafford on Sunday, after putting David Moyes' men ahead with a first-half header.
Van Persie has been plagued by the issue in the early stages of the season, and missed United's 1-0 home victory over Real Sociedad in the UEFA Champions League on October 23.
He will now sit out the Netherlands friendly encounters with Japan on Saturday, before their showdown with Colombia on Tuesday.
Van Persie - who captains the national side - became his country's record goalscorer when a hat-trick over Hungary in October took him to 41 goals, beating Patrick Kluivert's previous total of 40.
The former Arsenal man has seven Premier League goals to his name from 10 appearances this season.
Feyenoord midfielder Jordy Clasie will also be unavailable for Louis van Gaal's side with a foot problem.
To cover the injuries the Netherlands have called up Norwich City midfielder Leroy Fer and Vitesse's Davy Propper, with the latter in line to make his debut.
Van Gaal may take the opportunity to rotate his squad as he looks to settle on a regular starting XI ahead of the FIFA World Cup in Brazil next year.
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