The All Whites host Solomon Islands in Auckland next Friday with the return in Honiara the following Tuesday. The winner goes forward to an inter-continental playoff against a South American side for a spot in Russia next year.
West Ham United's Reid injured himself while warming up ahead of their Premier League match against Southampton at the weekend and would miss both ties, New Zealand Football said on Wednesday.
"He's been through a tough period with regards to injury and I know he's incredibly frustrated not to be playing for his club and for his country," coach Anthony Hudson said in a statement.
"But we wish him a quick recovery and hope to see him back with us in our next games.
"We have lost a world-class footballer, however I know that we have the quality within the squad to get the job done."
Striker Chris Wood, who has just moved from Leeds to Premier League Burnley, will stand in as captain for the two matches.
New Zealand, who reached the World Cup finals in 1982 and 2010, are heavy favourites to get past the Solomon Islanders but are likely to face heavyweights Argentina, Chile, Uruguay or Colombia in November's playoff.
(Reporting by Nick Mulvenney in Sydney, editing by Peter Rutherford)
