The 31-year-old Williamson also sat out the two-Test home series against Bangladesh last month due to the niggling elbow issue.
Trent Boult and Colin de Grandhomme made themselves unavailable for selection due to the prospect of further time in bio-secure bubbles and Managed Isolation.
The 36-year-old's selection as a "gold" pick for the Adelaide Strikers in Sunday's BBL draft presented a conflict with his central contract with New Zealand Cricket (NZC), which ran to next July.
Skipper Williamson cleared to play; spinner Patel included in 15-man squad
South Africa lost two wickets after tea but extended their lead over New Zealand to 211 runs by the close of Day 3 to leave the second Test delicately poised, in Christchurch, on Sunday.
Kane Williamson will miss the second Test against England after testing positive for COVID
Batsman Neil Broom has also been offered a contract after he was recalled to the national side following a lengthy absence to replace Ross Taylor while he recovered from eye surgery.
The player draft for the much-awaited Global T20 Canada 2023 was held in a hybrid-form in Mumbai.
Jacob Duffy, Blair Tickner, Rachin Ravindra and Hamish Rutherford were released from the initial 20 player squad.
Images from Day 1 of the first Test between England and New Zealand at Lord's on Thursday, June 2, 2022.
'There's no secret we're right in the hunt for the World Test Championship final following our two-nil win over India and having Trent and Kane fully fit and focussed for the upcoming series will be crucial.'
Captain Dimuth Karunaratne continued his rich vein of form to remain unbeaten on 49 with Angelo Mathews yet to score as only 36.3 overs of play were possible due to rain and bad light.
Injuries to frontline fast bowlers have forced New Zealand to opt for fresh blood in their pace attack for the three-match ODI series against India starting February 5 in Hamilton. Kyle Jamieson could be in for a potential debut, while Scott Kuggeleijn and Hamish Bennett return to the squad after a long absence. Injury has meant the likes of Trent Boult, Lockie Ferguson and Matt Henry are unavailable for the series.
Half centuries from Colin de Grandhomme and B J Watling gave New Zealand a first-innings lead of 138 against Sri Lanka on the fourth day of the second and final Test in Colombo on Sunday.
Latham, De Grandhomme lead NZ to series sweep of India
Australia's Marnus Labuschange struck another half century to pile on the runs and the misery over New Zealand on Day 3 of the day-night Test in Perth on Saturday. Earlier, Starc picked a five-wicket haul.
New Zealand opening batsman Martin Guptill has been dropped for the Test series against Pakistan and the uncapped Jeet Raval is poised to make his debut.
New Zealand all-rounder Colin de Grandhomme changed the script completely with a final over assault that enabled Royal Challengers Bangalore put up a healthy total against Mumbai Indians.
New Zealand's fast bowling department has been hit hard by injuries as Matt Henry, Doug Bracewell and Adam Milne have also been sidelined.
Ish Sodhi's 168-ball 56 not out helped New Zealand hold on for draw and secure a first series win over England since 1999.
Cricketing landscape is changing fast, need to strike balance: Williamson
Mohammed Siraj was given the responsibility to take RCB home and he repaid Skipper Kohli's trust.
Williamson's elbow injury kept him out of a Test match in India in December and home series against South Africa and Bangladesh.
India stormed back into the second and final Test on the back of some fine seam bowling on Sunday, tearing through New Zealand's top order to leave the hosts rocking on 142 for five at lunch on day two at Hagley Oval. Images from Day 2 of the second Test between New Zealand and India in Christchurch on Sunday.
Virat Kohli's top-ranked team, with 360 points in its kitty, is certainly the favourite on paper but the Black Caps under Kane Williamson are experts at wearing down opposition with their patience
England finished day two on 111-2 and trail New Zealand by 267 runs in the first innings of the first Test after Devon Conway's double ton took the game away from the home side on Thursday.
New Zealand, who beat England by 12 runs in their previous match, advanced to the February 21 final on net run rate. They had only needed to score 175 to have the superior run rate.
India win fifth ODI to seal 4-1 series victory in New Zealand
Images from Day 2 of the ICC World Test Championship Final between India and New Zealand, at The Hampshire Bowl, in Southampton, on Saturday.
New Zealand last toured Pakistan in 2003 for a white-ball series and since then have avoided touring the country because of security reasons.
Boult, De Grandhomme cleared to travel to Perth for first Test against Australia
Australia, who won the toss and batted in the day-nighter, reached 248 for four at stumps with Labuschagne 110 not out and Travis Head unbeaten on 20.
South Africa will need their bowlers to step up to keep their World Cup hopes alive.
Opting to field after Rohit Sharma won the toss, Mumbai bowled out Kolkata for a paltry 107 in 18.5 overs, and then chased down the target with 33 balls to spare at the Chinnaswamy Stadium.
New Zealand coach Gary Stead, on Tuesday, said he was a bit surprised by India's abject surrender in the first Test but is expecting a strong comeback in Christchurch.
With Kane Williamson likely to miss the Test, New Zealand will have a lot of work to do in the 3rd Test in Sydney.
Fast bowler Tim Southee will lead the Black Caps in the five matches against England starting in Christchurch on November 1.
Mustafizur Rahman's three-wicket haul and Mushfiqur Rahim's unbeaten 16-run knock helped Bangladesh defeat New Zealand by seven wickets in the first T20I of the five-match series here at the Shere Bangla National Stadium on Wednesday.
The West Indies are currently lying seventh in the 10-team standings with just three points in their kitty and they can't afford any further loss to stay in the mix for a semifinal spot.