The left-arm spinner suffered a right abductor strain during the first Test against West Indies, which New Zealand lost by nine wickets.
"Dan (Vettori) had some discomfort while in the field on day three of the first Test match with assessment confirming an adductor injury," Paul Close, the team's physiotherapist, said in a statement posted on the New Zealand Cricket website.
"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."
Former captain Vettori, 33, is New Zealand's most capped Test cricketer and will be crucial for the team when they tour India for a two-Test series starting August 23.