Guus Hiddink named his first squad since taking over from Louis van Gaal earlier this week, but has already made alterations to the group.
Tottenham goalkeeper Michel Vorm and Paris Saint-Germain defender Gregory van der Wiel have been dropped from the squad to make way for Afellay and Klaassen.
The return of Rafael van der Vaart headlined Hiddink's initial selection for next month's matches, which begin with a friendly against Italy on September 5.
Van der Vaart has not featured for the Netherlands since November 2013, a goalless friendly draw against Colombia.
The 31-year-old, who battled hamstring and calf problems last term, has scored seven goals in his last 12 national team appearances.
Van der Vaart is one of five members of Hiddink's squad who did not feature at the World Cup, with Erik Pieters and Jeroen Zoet, along with Afellay and Klaassen, also winning call-ups.
Goalkeepers: Jasper Cillessen (Ajax), Tim Krul (Newcastle United), Jeroen Zoet (PSV)
Defenders: Daley Blind (Ajax), Stefan de Vrij (Lazio), Daryl Janmaat (Newcastle United), Bruno Martins Indi (Porto), Erik Pieters (Stoke City), Paul Verhaegh (Augsburg), Ron Vlaar (Aston Villa), Joel Veltman (Ajax)
Midfielders: Ibrahim Afellay (Olympiacos), Jordy Clasie (Feyenoord), Nigel de Jong (Milan), Leroy Fer (QPR), Davy Klaasen (Ajax), Arjen Robben (Bayern Munich), Wesley Sneijder (Galatasaray), Rafael van der Vaart (Hamburg), Georginio Wijnaldum (PSV)
Forwards: Memphis Depay (PSV), Klaas-Jan Huntelaar (Schalke), Dirk Kuyt (Fenerbahce), Jeremain Lens (Dynamo Kiev), Robin van Persie (Manchester United)
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