Guus Hiddink had named the duo in his first squad since returning for a second spell as Netherlands coach following Louis van Gaal's exit.
However, Aston Villa centre-back Vlaar is unavailable due to a calf injury, while Feyenoord midfielder Clasie has a hamstring complaint.
In their place come Celtic centre-back Virgil van Dijk and Paris Saint-Germain full-back Gregory van der Wiel.
Van Dijk's call-up is the first time he has been selected by the national team, while Van der Wiel's last appearance for Netherlands came in a friendly encounter with France in March.
Hiddink now has a 23-man party, with the likes of Arjen Robben, Rafael van der Vaart and Klaas-Jan Huntelaar all available.
Netherlands will face Italy in a friendly in Bari on Thursday, before they begin their Euro 2016 qualifying campaign in the Czech Republic on September 9.