Scans confirmed the injury would require surgery, making it unlikely he will be fit and available for selection for the tournament in October and November.
IPL champions Gujarat Titans have signed Sri Lanka's white-ball captain Dasun Shanaka to replace New Zealander Kane Williamson.
Williamson injured his right knee in Friday's match while fielding near the boundary when he leapt to stop a six.
The 32-year-old got injured following a nasty fall while fielding on the boundary during the CSK innings.
'I'm sure he would be learning a lot from a number of leaders that he's been able to play under for a few years. He has a great understanding of the game,' said Williamson.
The present quartet of top batsmen emerged almost two decades after the retirement of the four great all-rounders.
The ground staff and authorities at Auckland and Wellington did an excellent job by preparing pitches of high quality.
After taking charge in 2016 Williamson captained New Zealand in 40 Tests - with 22 wins, 10 defeats and eight draws.
A maximum of 87 slots are now available with up to 30 being slotted for overseas players.
The home side chased down the 307-run target with 17 balls to spare, reaching 309 for 3 in 47.1 overs.