Pijnaker was expected to be among the centre backs named in coach Darren Bazeley's World Cup squad for the June 11 to July 19 finals in the U.S., Canada and Mexico.
Auckland FC confirmed Pijnaker's injury on Tuesday but said in a statement that the Netherlands-born 27-year-old would seek further opinion from a specialist.
Dislocated shoulders can take up to 16 weeks to heal. New Zealand open their World Cup campaign against Iran on June 15.
Pijnaker joins injured New Zealand defenders Michael Boxall, Tommy Smith, Liberato Cacace and Francis de Vries on the sidelines, while midfielder Sarpreet Singh is also nursing a knee problem.
There was also better news for Bazeley over the weekend as Chris Wood, New Zealand's captain and top goal-scorer, played his first match in nearly six months in Nottingham Forest's 1-1 Premier League draw with Aston Villa after recovering from knee surgery.
New Zealand will also play Egypt and Belgium in the World Cup's group stage as the All Whites return to the tournament for the first time since South Africa 2010.