New Zealand, who are currently playing a Test series against West Indies, will be without their lead spinner as he was ruled out for the second Test starting on Friday.
New Zealand will play two Tests in India, starting on August 23 in Hyderabad. The second Test is in Bangalore from August 31. Wicketkeeper-batsman Brendon McCullum said he would "comeback after in a couple of months' time" which means he is unlikely for India tour.
McCullum said it was a "huge loss" to miss out on Vettori's services.
"It's a huge loss, not just for his performance on the field which he has done for a number of years consistently - he has really led us from that point of view - but also what he offers us in the changing room," McCullum was quoted as saying.
"He's had a phenomenal career so far and we hope he rests up, gets himself recuperated and he comes back in a couple of months' time for us and we're able to gel him back into a team that is performing a bit better than of late," the wicketkeeper added.
Team's physiotherapist, Paul Close was quoted in the media, saying: "Dan had some discomfort while in the field on day three of the first Test match with assessment confirming an adductor injury."
He added: "It was managed during the match but further assessment has indicated he will not be fully fit in time for the next test. Dan will return to New Zealand where here will be monitored closely and undergo a period of rehabilitation. He will require a rest from bowling and his return date will be determined by how well he responds to the treatment."