The Royal Dutch Football Association (KNVB) said in a statement that the 27-year-old Roma player "would not be fit in time" for the matches.
Argentina, Chile flounder in World Cup qualifiers
Head coach Dick Advocaat has not called up a replacement, as he looks to help the Dutch avoid missing out on back-to-back major tournaments for the first time in 32 years.
The three-time World Cup runners-up are third in Group A of European qualifying, four points adrift of leaders France and three behind second-placed Sweden.
Chile pin hope on Pinilla for World Cup qualifiers
They travel to Belarus on Saturday, before a potential straight fight for a play-off spot with Sweden in Amsterdam on Tuesday.
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