Williamson's hip has been troubling him for some time now - it was because of this same problem that the 29-year-old had to midway abandon the Test series against Bangladesh in March.
"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," said Black Caps coach Gary Stead.
"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.
Southee had earlier led New Zealand to a T20I series win in Sri Lanka in September.
"We're fortunate to have someone experienced like Tim who can comfortably step in and take the reins, as he successfully did on the recent tour of Sri Lanka," said Stead.
The first match of the series will be played in Christchurch on November 1. The two teams will then play two Tests after the conclusion of the T20I series.
New Zealand T20I squad:
Tim Southee (c), Trent Boult (for the final two matches), Colin de Grandhomme, Lockie Ferguson (for the first three matches), Martin Guptill, Scott Kuggeleijn, Daryl Mitchell, Colin Munro, Jimmy Neesham, Mitchell Santner, Tim Seifert, Ish Sodhi, Ross Taylor, Blair Tickner.