Fast bowler Tim Southee will lead the Black Caps in the five matches against England starting in Christchurch on November 1.
“We’ve been monitoring the injury for a while now and it’s the same issue that ruled him out of the final test against Bangladesh back in March," New Zealand coach Gary Stead told the NZC website.
“It’s disappointing timing for Kane at the start of an exciting Kiwi summer, but we feel it’s the right decision with a busy season ahead."
Fast bowler Blair Tickner was named in the New Zealand squad after making his debut against India this year.
New Zealand host England in a two-test series starting at Tauranga on November 20.
T20 squad: Tim Southee (captain), Trent Boult (games four and five), Colin de Grandhomme, Lockie Ferguson (games one, two and three), Martin Guptill, Scott Kuggeleijn, Daryl Mitchell, Colin Munro, Jimmy Neesham, Mitchell Santner, Tim Seifert (wicketkeeper), Ish Sodhi, Ross Taylor, Blair Tickner
