Team spokesman Jamie Scott said the midfielder, who plays for English premier league side Blackburn Rovers, did not travel to Nelspuit, about 400 east of Johannesburg, for the game.
"He's got a bit of an ear infection and saw a doctor yesterday but he'll be fine for the 15th," he said. "He's still at the base camp (near Johannesburg). There was no point in putting him on an aeroplane."
The 32-year-old New Zealand Footballer of the Year is central to the All Whites side and would lead the team against Slovakia on Tuesday.
Fellow World Cup hopefuls Chile won the friendly 2-0, with goals from Gonzalo Fierro and Esteban Paredes.
Earlier New Zealand's chances in the globe's most watch tournament - which starts on Friday - received a boost with the news that vice-captain and midfielder Tim Brown would join the squad on Thursday after recovering from a shoulder fracture.
The All Whites, ranked a lowly 78th and in their second World Cup, also play defending champions Italy on June 20 and Paraguay on June 24.
