New Zealand Cricket announced on Wednesday that Williamson would stay home and rehabilitate the injury rather than head off with teammates to the subcontinent on Friday.
The three-Test series begins on October 16 in Bengaluru, with selector Sam Wells all but ruling out Williamson from the opening Test.
"The advice we've received is that the best course of action is for Kane to rest and rehabilitate now, rather than risk aggravating the injury," Wells said.
"We're hopeful that if the rehabilitation goes to plan, Kane will be available for the latter part of the tour."
Mark Chapman has come into the squad as cover for Williamson, considered New Zealand's best ever batter but synonymous with injury in recent years.
The 34-year-old struggled with a chronic elbow issue in 2021 and 2022, then in April 2023 he suffered a ruptured anterior cruciate ligament while on Indian Premier League duty.
He made a swift comeback for the ODI World Cup, only to break his thumb in his return match against Bangladesh and miss much of that tournament.
In January Williamson missed home white-ball internationals with a hamstring injury on the same leg.
The fresh setback confirms New Zealand's status as firm underdogs for the series, which concludes with Tests in Pune and Mumbai.
While India have claimed a record-extending 18 straight Test series at home by beating Bangladesh, few of the current Black Caps squad were even alive for their last win in India.
New Zealand have not won there since 1988 - one of only two Test victories away to the superpower.
The Black Caps also enter the series fresh from a 2-0 series loss to Sri Lanka in Galle.
The second Test was a particularly humbling experience, with Sri Lanka declaring at 5-602 before skittling New Zealand for 88 on their way to a huge innings victory.
Tim Southee resigned as skipper after that series defeat, with Tom Latham to pick up the reins in India.
Michael Bracewell will play the first Test only before returning to New Zealand for the birth of his second child, with India-born spinner Ish Sodhi to replace him.
NEW ZEALAND SQUAD FOR INDIA TESTS:Â
Tom Latham (capt), Tom Blundell, Michael Bracewell, Mark Chapman, Devon Conway, Matt Henry, Daryl Mitchell, Will O'Rourke, Ajaz Patel, Glenn Phillips, Rachin Ravindra, Mitchell Santner, Ben Sears, Ish Sodhi, Tim Southee, Kane Williamson, Will Young
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