Tom Latham, who skippered in the recent series with Bangladesh - which 31-year-old Williamson also missed - will again lead the team.
All-rounder Colin de Grandhomme and opener Hamish Rutherford have been recalled in a 15-man squad for the opening Test. Uncapped pair wicketkeeper Cam Fletcher and fast bowler Blair Tickner were also named.
Seamer Trent Boult is unavailable as he awaits the birth of his third child.
The first Test starts at Christchurch's Hagley Oval on February 17.
"(Kane) was desperate to be fit for the series but with the amount of loading required for Test cricket, we had to make the tough call... and focus on returning for the white-ball matches against Netherlands in March," said Kiwi head coach Gary Stead.
"It's important to remember this squad is just for the first Test so we do have flexibility to make changes as required, with the likes of Trent and Ajaz [Patel] potentially available for the second," added Stead.
First Test squad: Tom Latham (captain), Tom Blundell, Devon Conway, Colin de Grandhomme, Cam Fletcher, Matt Henry, Kyle Jamieson, Daryl Mitchell, Henry Nicholls, Rachin Ravindra, Hamish Rutherford, Tim Southee, Blair Tickner, Neil Wagner, Will Young.
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