Kane Williamson suffered a fractured thumb in Friday's World Cup victory over Bangladesh and will be sidelined until the latter stages of the tournament.
New Zealand maintained their perfect start to the World Cup as they eased to a comfortable eight-wicket win over Bangladesh in Chennai.
England's World Cup defence began with a punishing nine-wicket defeat in Ahmedabad as New Zealand helped themselves to a slice of revenge.
The Proteas are set to tour New Zealand to take on the hosts in a two-match Test series in February next year.
Kane Williamson hit an unbeaten century to guide New Zealand to a last-ball victory over Sri Lanka in the first Test in Christchurch.
England lost one of the tightest finishes in Test history, downed by a solitary run in Wellington as New Zealand became just the fourth side ever to win a game after following on.