Striker Robin van Persie, due to have surgery to remove a wisdom tooth, was included in a 22-man squad named by coach Bert van Marwijk on Friday.
"Sneijder's hamstring injury has upset our plans as he is one of the players who can translate exactly on the pitch how we want to play," Van Marwijk told reporters.
"We expect Robin (van Persie) to join the squad on Tuesday although there are no guarantees."
Twente Enschede winger Eljero Elia is the only new name in the squad, called up after an impressive season in which he attracted the attention of several top European teams.
"We have been following Elia for months and he made a positive impression the last days during our training camp," said Van Marwijk.
The Netherlands will travel to Iceland on June 6 and host Norway four days later in Rotterdam.
The Dutch lead Group Nine with 15 points after five matches, and need one more win to qualify for the World Cup finals next year in South Africa.
Squad:
Goalkeepers: Maarten Stekelenburg (Ajax Amsterdam), Henk Timmer (Feyenoord).
Defenders: John Heitinga (Atletico Madrid), Joris Mathijsen (Hamburg SV), Dirk Marcelis (PSV Eindhoven), Andre Ooijer (Blackburn Rovers), Edson Braafheid (Twente Enschede), Gregory van der Wiel (Ajax Amsterdam), Giovanni van Bronckhorst (Feyenoord), Khalid Boulahrouz (VfB Stuttgart).
Midfielders: Mark van Bommel (Bayern Munich), Nigel de Jong (Manchester City), Rafael van der Vaart (Real Madrid), Demy de Zeeuw (AZ Alkmaar), Stijn Schaars (AZ Alkmaar), David Mendes da Silva (AZ Alkmaar).
Forwards: Dirk Kuyt (Liverpool), Robin van Persie (Arsenal), Ryan Babel (Liverpool), Klaas Jan Huntelaar (Real Madrid), Arjen Robben (Real Madrid), Eljero Elia (Twente Enschede).
