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.
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.
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.
