New Zealand play a two-Test series against India starting August 23 and Ross Taylor will lead the side in the absence of Vettori.
"Unfortunately Daniel Vettori won't recover in time for the Test series but his injury has created and opportunity for Jeetan Patel to come back into the side. Jeetan has been in great from for Warwickshire and deserves his opportunity," National Selection Manager Kim Littlejohn said.
All-rounder James Franklin has been included in the squad in place of off-colour batsman Dean Brownlie.
"He brings a lot of experience and knowledge of playing in Indian conditions which will be invaluable," said Littlejohn.
"Dean Brownlie misses out on selection. We continue to see him as player of the future but at this stage we feel he needs to works on parts of his game. There's no doubt he will work hard to regain selection," he added.
Brownlie averaged just 15.75 as New Zealand lost 2-0 in a Test series against the West Indies recently.
The squad: Ross Taylor (c), Trent Boult, Doug Bracewell, Daniel Flynn, James Franklin, Martin Guptill, Chris Martin, Brendon McCullum, Tarun Nethula, Jeetan Patel, Tim Southee, Kruger van Wyk, Neil Wagner, BJ Watling, Kane Williamson.