The Liverpool man donned the captain's armband in Friday's 4-1 success over Belgium but has now been granted leave to go on holiday after a gruelling domestic season.
Van Gaal should otherwise be working with a full selection of players, and it would not be a shock to see Oranje make a number of alterations as Wales prepare to do the same.
Mark Flekken is a candidate to wrestle the goalkeeping gloves off Jasper Cillessen, as Matthijs de Ligt and Stefan de Vrij prepare to man the backline in Van Dijk's absence.
Denzel Dumfries will likely hold his spot on the right, but Tyrell Malacia can expect to be drafted in on the opposite flank in order to give Daley Blind's legs a much-needed rest.
Frenkie de Jong, Davy Klaassen and Steven Berghuis could all form an unchanged midfield unit, though, as Memphis Depay seeks to go level with Klaas-Jan Huntelaar on 42 goals for the Netherlands.
Vincent Janssen could be back in the squad after his wedding, but Cody Gakpo may be selected to partner Depay this week, in spite of Steven Bergwijn's strike against the Red Devils.
Netherlands possible starting lineup: Flekken; De Ligt, Timber, De Vrij; Dumfries, De Jong, Klaassen, Malacia; Berghuis; Depay, Gakpo