Williamson, the third ranked Test batsman in the world, missed the recent Twenty20 series with the problem but is fit to lead a 15-man squad in the two-Test series.
The 29-year-old will captain his side in the first Test at his home ground in Mount Maunganui, starting on November 21, and selector Gavin Larsen is delighted to have him available.
“Kane’s made good progress over the past fortnight and we’re delighted to welcome back a player of his class and experience,” Larsen said.
“It’s obviously going to be a very special Test for him and Trent Boult, being such passionate locals - we know there’s already a lot of excitement in that part of the Bay of Plenty.”
New Zealand have also handed a first Test call-up to paceman Lockie Ferguson, in one of two changes from the squad which toured Sri Lanka - with leg-spinner Todd Astle also included.
Ferguson was the second leading wicket-taker in the summer’s World Cup - where New Zealand finished runners-up to England.
“There’s no doubt Lockie has been knocking on the door for a while now and we’re delighted to finally bring him into the Test fold,” Larsen added.
“It’s well documented he has raw pace, but he also possesses a quality bowling skill set and has proven durability to stay on the park.”
Astle is included alongside Mitchell Santner, with the pair preferred to Will Somerville and Ajaz Patel as spin options.