The 35-year-old former captain turned down a central contract with New Zealand Cricket for this season and also missed the home T20 series against Australia earlier this month, which the Black Caps lost 2-0.
"Kane had to overcome a minor medical issue in the past month, and we both agreed he needs some more time to get himself physically ready to return," coach Rob Walter said.
"He's obviously a world-class player and we're hoping these two weeks will ensure he's ready for the ODIs against England and the following tour by the West Indies."
New Zealand play England in T20s in Christchurch on October 18 and 20 before the third match at Auckland's Eden Park on October 23. They also play a three-match one-day international series against the tourists in late October and early November.
Pace bowler Ben Sears will also miss the T20 series after suffering a hamstring tear in training last week that will require surgery.
Spinner Mitch Santner, who replaced Williamson as white-ball captain in December last year, returns to the squad after abdominal surgery.
Also back is allrounder Rachin Ravindra, who missed the Australia series with a facial injury. Jimmy Neesham retains his spot in the squad after impressing against the Australians as Ravindra's replacement.
"It's great to have Mitch back," said Walter.
"Alongside being our leader, he's one of the very best white-ball spinners in the world and his skills and experience will be a welcome addition.
"Likewise, it's nice to welcome back Rachin who was unlucky to miss out on Australia and I know is really excited for this series."
BLACK CAPS SQUAD:
Mitchell Santner (capt), Michael Bracewell, Mark Chapman, Devon Conway, Jacob Duffy, Zak Foulkes, Matt Henry, Bevon Jacobs, Kyle Jamieson, Daryl Mitchell, Jimmy Neesham, Rachin Ravindra, Tim Robinson, Tim Seifert.
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